0 .}, number={2}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1981}, month={Apr}, pages={507–510} } @article{campbell_silverstein_1981, title={A nonlinear system with singular vector field near equilibria}, volume={12}, ISSN={0003-6811 1563-504X}, url={http://dx.doi.org/10.1080/00036818108839348}, DOI={10.1080/00036818108839348}, abstractNote={The system Nω=(N-α)ω+y, N= bN+aωωT, N(t)∊Rm×m, ω(t)∊Rm which originally arose from a model for the pathological behavior of neural networks, is studied. Similar equations can arise in a variety of applications. It is shown that if N(0) is positive definite, then solutions exist for all time. Equilibrium points are determined. N is found to be singular at the equilibrium points, making the analysis of the asymptotic properties of the system non-trivial. The asymptotic behavior when y = 0 is completely described. Some results are proven on the asymptotic behavior of N and ω when y≠0}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Silverstein, Jack W.}, year={1981}, month={Jan}, pages={57–71} } @article{campbell_1981, title={A procedure for analyzing a class of nonlinear semistate equations that arise in circuit and control problems}, volume={28}, ISSN={0098-4094}, url={http://dx.doi.org/10.1109/tcs.1981.1084966}, DOI={10.1109/tcs.1981.1084966}, abstractNote={Some circuits not possessing a state-variable represenation may admit semistate equations of the form Ax(t)+B(x(t))=f(t) where x , f are vector functions, A is a singular constant matrix, and B is a nonlinear vector valued function. Some nonlinear optimal control problems, in which certain combinations of controls are either "cheap" or free, also lead to equations in this form. In this paper we show how In many cases of interest It is possible to solve a singular linear subsystem and use this solution to reduce the problem to a smaller order nonsingular, nonlinear system.}, number={3}, journal={IEEE Transactions on Circuits and Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1981}, month={Mar}, pages={256–261} } @article{campbell_poole_1981, title={Computing nonnegative rank factorizations}, volume={35}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(81)90272-x}, DOI={10.1016/0024-3795(81)90272-x}, abstractNote={The existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered. An algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1-inverse exists.}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Poole, George D.}, year={1981}, month={Feb}, pages={175–182} } @article{campbell_poole_1981, title={Convergent regular splittings for nonnegative matrices}, volume={10}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088108817393}, DOI={10.1080/03081088108817393}, abstractNote={MP matrices are those real matrices which possess a nonnegative, nonsingular l-inverse. This paper characterizes the nonnegative MP matrices and hence, determines when a nonnegative matrix A has a convergent regular splitting M—Q which induces the linear stationary iterative scheme x k+1=M −1 Qxk +M −1 b to solve Ax=b.}, number={1}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Poole, George D.}, year={1981}, month={Feb}, pages={63–73} } @inproceedings{campbell_1981, title={Numerical procedures for analyzing nonlinear semi-state equations}, booktitle={Proceedings Fifth International Symposium on the Mathematical Theory of Networks and Systems}, author={Campbell, Stephen L.}, year={1981}, pages={22–27} } @article{campbell_1981, title={On an assumption guaranteeing boundary layer convergence of singularly perturbed systems}, volume={17}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/0005-1098(81)90038-8}, DOI={10.1016/0005-1098(81)90038-8}, abstractNote={In a recent paper by B. A. Francis, an assumption was made that guaranteed convergence in the boundary layer for singularly perturbed linear systems, but the assumption was not discussed. This note examines this assumption in some detail. Verifiable sufficient and necessary conditions are given. Illustrative examples are presented.}, number={4}, journal={Automatica}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1981}, month={Jul}, pages={645–646} } @article{campbell_clark_1981, title={Order and the index of singular time-invariant linar systems}, volume={1}, ISSN={0167-6911}, url={http://dx.doi.org/10.1016/s0167-6911(81)80048-5}, DOI={10.1016/s0167-6911(81)80048-5}, abstractNote={Various concepts of order have been proposed in the literature. It is shown that many of these are directly related to the index of a system.}, number={2}, journal={Systems & Control Letters}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Clark, Kenneth}, year={1981}, month={Aug}, pages={119–122} } @article{campbell_1980, title={Continuity of The Drazin inverse}, volume={8}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088008817329}, DOI={10.1080/03081088008817329}, abstractNote={Let A be an n×n matrix. It is shown that if a matrix Â comes close to satisfying the definition of the Drazin inverse of A,AD , then Â is close to AD .}, number={3}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1980}, month={Feb}, pages={265–268} } @article{campbell_1980, title={Linear operators for which T*T and TT* commute III}, volume={91}, number={1}, journal={Pacific Journal of Mathematics}, author={Campbell, Stephen L.}, year={1980}, pages={39–45} } @article{campbell_faulkner_1980, title={Operators on Banach spaces with complemented ranges}, volume={35}, ISSN={0001-5954 1588-2632}, url={http://dx.doi.org/10.1007/bf01896831}, DOI={10.1007/bf01896831}, number={1-2}, journal={Acta Mathematica Academiae Scientiarum Hungaricae}, publisher={Springer Science and Business Media LLC}, author={Campbell, S. L. and Faulkner, G. D.}, year={1980}, month={Mar}, pages={123–128} } @article{campbell_1980, title={Singular linear systems of differential equations with delays}, volume={11}, ISSN={0003-6811 1563-504X}, url={http://dx.doi.org/10.1080/00036818008839326}, DOI={10.1080/00036818008839326}, abstractNote={The differential equation Ax + Bx = Cx(t-l) + f is studied where A, B, C are square matrices. All matrices are allowed to be singular. Examples are given to show that not all initial functions are consistent and that for consistent initial conditions, solutions may be continuous for only a finite time period. Solutions are given explicitly by a recursion formula and consistent initial conditions are explicitly characterized}, number={2}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1980}, month={Jan}, pages={129–136} } @inproceedings{campbell_1979, title={A functional analytic approach to autonomous linear singular perturbation problems}, booktitle={Proceedings of the Seventeenth Annual Allerton Conference on Communication, Control, and Computing}, author={Campbell, Stephen L.}, year={1979}, pages={445–463} } @article{campbell_faulkner_gardner_1979, title={Isometries on L^p Spaces and Copies of L^p shifts}, volume={77}, ISSN={0002-9939 1088-6826}, DOI={10.2307/2042638}, number={2}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Faulkner, G.D. and Gardner, M.L.}, year={1979}, month={Nov}, pages={198–200} } @inbook{campbell_faulkner_sine_1979, place={San Francisco, California}, series={Research notes in mathematics}, title={Isometries, projections and Wold decompositions}, ISBN={9780822484509 9780273084501}, booktitle={Operator Theory and Functional Analysis}, publisher={Pitman Publishing Company}, author={Campbell, Stephen L. and Faulkner, G.D. and Sine, Robert}, editor={Erdelyi, IvanEditor}, year={1979}, pages={84–114}, collection={Research notes in mathematics} } @article{campbell_1979, title={Limit behavior of solutions of singular difference equations}, volume={23}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(79)90100-9}, DOI={10.1016/0024-3795(79)90100-9}, abstractNote={Necessary and sufficient conditions for a solution {zk} of the difference equation Azk+1+Bzk = b, k ⩾0, with A singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, A = A+B, are given first. In particular, the case when A = A∗ and A is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed.}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1979}, month={Feb}, pages={167–178} } @article{campbell_1979, title={Nonregular Singular Dynamic Leontief Systems}, volume={47}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1914020}, DOI={10.2307/1914020}, number={6}, journal={Econometrica}, publisher={JSTOR}, author={Campbell, Stephen L.}, year={1979}, month={Nov}, pages={1565} } @article{campbell_1979, title={On a singularly perturbed autonomous linear control problem}, volume={24}, ISSN={0018-9286}, url={http://dx.doi.org/10.1109/tac.1979.1101951}, DOI={10.1109/tac.1979.1101951}, abstractNote={A singularly perturbed autonomous control process is examined. The relationship between the original and the reduced problem is developed.}, number={1}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1979}, month={Feb}, pages={115–117} } @article{campbell_rose_1979, title={Singular Perturbation of Autonomous Linear Systems}, volume={10}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0510051}, DOI={10.1137/0510051}, abstractNote={Let $X_\varepsilon (t) = \exp (({{A + B} /\varepsilon })t)$ where A, B are $n \times n$ matrices. It is shown that $X_\varepsilon (t)$ converges pointwise for $t > 0$ as $\varepsilon \to 0^ + $ if and only if Index $B \leqq 1$ and the nonzero eigenvalues of B have negative real part. An explicit representation of the limit of $X_\varepsilon (t)$ is given. These results are applied to the singularly perturbed system $\dot x = A_1 (\varepsilon )x + A_2 (\varepsilon )y$, $\varepsilon \dot y = B_1 (\varepsilon )x + B_2 (\varepsilon )y$. This paper differs from earlier work both in the derivation of necessary and sufficient conditions and in the explicit forms for the limits.}, number={3}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Rose, Nicholas J.}, year={1979}, month={May}, pages={542–551} } @article{campbell_daughtry_1979, title={The stable solutions of quadratic matrix equations}, volume={74}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Daughtry, John}, year={1979}, pages={19–23} } @article{campbell_1978, title={Linear operators for which T∗T and T + T∗ commute. III}, volume={76}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1978.76.17}, DOI={10.2140/pjm.1978.76.17}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1978}, month={May}, pages={17–19} } @article{campbell_gupta_1978, title={On k-quasihyponormal operators}, volume={23}, journal={Mathematica Japonica}, author={Campbell, Stephen L. and Gupta, B.C.}, year={1978}, pages={185–189} } @article{campbell_1978, title={On the limit of a product of matrix exponentials}, volume={6}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081087808817221}, DOI={10.1080/03081087808817221}, abstractNote={The existence of the limit as ϵ→0 exp[(A+B/ϵ)t] exp[-Bt/ϵ]is studied for n×n matrices A,B. Necessary and sufficient conditions on B that the limit exist for all A are given.}, number={1}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1978}, month={Jan}, pages={55–59} } @article{campbell_1978, title={Optimal control of discrete linear processes with quadratic cost}, volume={9}, ISSN={0020-7721 1464-5319}, url={http://dx.doi.org/10.1080/00207727808941742}, DOI={10.1080/00207727808941742}, abstractNote={A direct method 18 given for solving the optimal control problem Xk+1+ Bukk=0,,N — l with quadratic cost functional. The matrices A, B,,Q, H are all allowed to be singular. The process is not assumed to be completely controllable. The coefficients are assumed to have the property that there exists a scalar μ such that Q + B ∗( — μA∗+I)−1-μH(μ — A)−1 B is invertible.}, number={8}, journal={International Journal of Systems Science}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1978}, month={Aug}, pages={841–847} } @article{campbell_rose_1978, title={Singular perturbation of autonomous linear systems III}, volume={44}, journal={Houston Journal of Mathematics}, author={Campbell, Stephen L. and Rose, N.J.}, year={1978}, pages={527–539} } @article{campbell_1978, title={Singular perturbation of autonomous linear systems, II}, volume={29}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/0022-0396(78)90046-3}, DOI={10.1016/0022-0396(78)90046-3}, abstractNote={This paper is concerned with determining the limit of exp(A + Bϵ + Cϵr + Eϵs)t for t > 0, where A, B, C, E are n × n complex matrices, and s > r > 1. Explicit expressions are derived for the limit under a variety of assumptions. Examples are given to justify some of these assumptions. The application of these limit theorems to singularly perturbed antonomous linear systems is discussed.}, number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Campbell, Stephen L}, year={1978}, month={Sep}, pages={362–373} } @article{campbell_meyer_1978, title={Weak Drazin inverses}, volume={20}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(78)90048-4}, DOI={10.1016/0024-3795(78)90048-4}, abstractNote={A new type of generalized inverse is defined which is a weakened form of the Drazin inverse. These new inverses are called (d)-inverses. Basic properties of (d)-inverses are developed. It is shown that (d)-inverses are often easier to compute than Drazin inverses and can frequently be used in place of the Drazin inverse when studying systems of differential equations with singular coefficients or when studying Marcov chains.}, number={2}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Meyer, Carl D., Jr.}, year={1978}, pages={167–178} } @article{campbell_1977, title={Linear Systems of Differential Equations with Singular Coefficients}, volume={8}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0508081}, DOI={10.1137/0508081}, abstractNote={Differential equations of the form $A\dot x + Bx = f$ are studied where A, B are $m \times n$ matrices. Explicit solutions are derived for several cases of interest. One such case is when there exists a scalar $\lambda $ such that $\lambda A + B$ is of full rank. Another includes the case when A, B are normal matrices and one is positive semidefinite. The application of these results to linear autonomous control processes is discussed.}, number={6}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1977}, month={Nov}, pages={1057–1066} } @article{campbell_geller_1977, title={Linear operators for which T*T and T+T* commute II}, volume={226}, journal={Transactions of the American Mathematical Society}, author={Campbell, Stephen L. and Geller, R.}, year={1977}, pages={305–319} } @article{campbell_gellar_1977, title={On asymptotic properties of several classes of operators}, volume={66}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Gellar, R.}, year={1977}, pages={79–84} } @article{campbell_1977, title={On continuity of the Moore-Penrose and Drazin generalized inverses}, volume={18}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(77)90079-9}, DOI={10.1016/0024-3795(77)90079-9}, abstractNote={Let A be an m × n matrix. It is shown that if a matrix comes close to satisfying the definition of the Moore-Penrose generalized inverse of A,A†, then ┆–A†┆ is small. Norm estimates are given which make precise what is close. The Drazin generalized inverse is also considered.}, number={1}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1977}, pages={53–57} } @article{campbell_meyer, jr._rose_1976, title={Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients}, volume={31}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0131035}, DOI={10.1137/0131035}, abstractNote={Let A, B be $n \times n$ matrices, f a vector-valued function. A and B may both be singular. The differential equation $Ax' + Bx = f$ is studied utilizing the theory of the Drazin inverse. A closed form for all solutions of the differential equation is given when the equation has unique solutions for consistent initial conditions.}, number={3}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Meyer, Jr., Carl D. and Rose, Nicholas J.}, year={1976}, month={Nov}, pages={411–425} } @article{campbell_1976, title={Differentiation of the Drazin Inverse}, volume={30}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0130062}, DOI={10.1137/0130062}, abstractNote={Suppose that A is an $n \times n$ matrix of differentiable functions. Suppose that $A^D $ is defined as $A^D (t) = [ {A(t)} ]^D $ , where $[ {A(t)} ]^D $ is the Drazin inverse of the $n \times n$ matrix $A(t)$. A formula is derived for the derivative of $A^D $ in terms of A, $A^D $ and the derivative of A. The conditions under which $A^D $ is differentiable are discussed.}, number={4}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Jun}, pages={703–707} } @article{campbell_1976, title={Optimal Control of Autonomous Linear Processes with Singular Matrices in the Quadratic Cost Functional}, volume={14}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/0314068}, DOI={10.1137/0314068}, abstractNote={The optimal control of the autonomous linear process $\dot x = Ax + Bu$ with quadratic cost functional is studied. The initial and terminal times and positions are fixed. The matrices in the cost functional are allowed to be singular. An assumption, weaker than invertibility, is placed on the coefficient matrices. Under this assumption, necessary and sufficient conditions are given for the existence of an optimal control in terms of the initial and final position of the process. A closed form for the optimal control is given.}, number={6}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Nov}, pages={1092–1106} } @inproceedings{campbell_1976, title={Optimal control of autonomous linear processes with singular matrices in the quadratic cost functional II}, url={http://dx.doi.org/10.1109/cdc.1976.267733}, DOI={10.1109/cdc.1976.267733}, abstractNote={The optimal control of the autonomous linear process X = Ax + Bu with quadratic cost functional is studied. Initial and terminal times and positions are fixed. An assumption, weaker than invertibility, is placed on the matrices involved. A closed form for the optimal control is given. The extension of the method to other problems is discussed, including infinite systems and discrete problems.}, booktitle={1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes}, publisher={IEEE}, author={Campbell, S.}, year={1976}, month={Dec} } @article{campbell_geller_1976, title={Spectral properties of linear operators for which T*T and T + T* commute}, volume={60}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Geller, R.}, year={1976}, pages={197–202} } @article{campbell_1976, title={The Drazin Inverse of an Infinite Matrix}, volume={31}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0131043}, DOI={10.1137/0131043}, abstractNote={Let $A = [ {a_{ij} } ]$, $0\leqq i < \infty $, $0\leqq j < \infty $. Then A is called a denumerably infinite matrix. A way to define a Drazin inverse for A is presented. The application of this definition to denumerable Markov chains, infinite linear systems of differential equations, and linear operators on Banach spaces is discussed.}, number={3}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Nov}, pages={492–503} } @article{campbell_meyer_1975, title={Continuity properties of the Drazin pseudoinverse}, volume={10}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(75)90097-x}, DOI={10.1016/0024-3795(75)90097-x}, abstractNote={Let BD denote that Drazin inverse of the n×n complex matrix B. Define the core-rank of B as rank (Bi(B)) where i(B) is the index of B. Let j = 1,2,…, and Aj and A be square matrices such that Ai converges to A with respect to some norm. The main result of this paper is that AjD converges to AD if and only if there exist a j0 such that core-rank Aj=core-rankA for j ⩾ j0.}, number={1}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Meyer, Carl D., Jr.}, year={1975}, month={Feb}, pages={77–83} } @article{campbell_meyer_1975, title={EP Operators and Generalized Inverses}, volume={18}, ISSN={0008-4395 1496-4287}, url={http://dx.doi.org/10.4153/cmb-1975-061-4}, DOI={10.4153/cmb-1975-061-4}, abstractNote={AbstractThe relationship between properties of the generalized inverse of A, A†, and of the adjoint of A, A*, are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EPr. A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.}, number={3}, journal={Canadian Mathematical Bulletin}, publisher={Canadian Mathematical Society}, author={Campbell, Stephen L. and Meyer, Carl D.}, year={1975}, month={Aug}, pages={327–333} } @article{campbell_1975, title={Linear operators for which T∗T and T + T∗ commute}, volume={61}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1975.61.53}, DOI={10.2140/pjm.1975.61.53}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1975}, month={Nov}, pages={53–57} } @article{campbell_1975, title={Operator-valued inner functions analytic on the closed disc. II}, volume={60}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1975.60.37}, DOI={10.2140/pjm.1975.60.37}, abstractNote={An operator-valued inner function V is called scalar if {V(w): I w I < 1} is a commuting family of normal operators.Suppose that T is a bounded linear operator with || T\\ ^ 1 and spectral radius strictly less than one.Let V τ be its Potapov inner function and define U τ = V τ Vj{ί).The structure of nonnormal T for which U τ is scalar is discussed.An explicit characterization is given if the underlying Hubert space is finite dimensional.Examples are given for the infinite dimensional case.The relationship between scalar inner functions and operators for which T*T and T* + T commute is examined.}, number={2}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1975}, month={Oct}, pages={37–49} } @article{campbell_1975, title={Subnormal operators with nontrivial quasinormal extensions}, volume={37}, number={3-4}, journal={Acta Scientiarum Mathematicarum}, author={Campbell, Stephen L.}, year={1975}, pages={191–193} } @article{campbell_1974, title={Commutation properties of the coefficient matrix in the differential equation of an inner function}, volume={42}, number={2}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L.}, year={1974}, pages={507–512} } @article{campbell_1974, title={Linear operators for which T∗T and TT∗ commute. II}, volume={53}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1974.53.355}, DOI={10.2140/pjm.1974.53.355}, number={2}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1974}, month={Aug}, pages={355–361} } @article{carmpbell_1972, title={Inner functions analytic at a point}, volume={16}, ISSN={0019-2082}, url={http://dx.doi.org/10.1215/ijm/1256065547}, DOI={10.1215/ijm/1256065547}, number={4}, journal={Illinois Journal of Mathematics}, publisher={Duke University Press}, author={Carmpbell, Stephen L.}, year={1972}, month={Dec}, pages={651–652} } @article{campbell_1972, title={Linear operators for which T*T and TT* commute}, volume={34}, journal={Proc. American Mathematical Society}, author={Campbell, Stephen L.}, year={1972}, pages={177–180} } @article{campbell_1972, title={Operator-valued inner functions analytic on the closed disc}, volume={41}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1972.41.57}, DOI={10.2140/pjm.1972.41.57}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1972}, month={Apr}, pages={57–62} } @article{campbell_1972, title={The exponential representation of operator valued, differentiable inner functions}, volume={12}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/0022-0396(72)90018-6}, DOI={10.1016/0022-0396(72)90018-6}, number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Campbell, Stephen L}, year={1972}, month={Nov}, pages={455–461} }