Format:
Online-Ressource (X, 368 p. 22 illus., 15 illus. in color, digital)
ISBN:
9783034804110
Series Statement:
Operator Theory: Advances and Applications 222
Content:
Preface -- Inroduction (an overview of the contents of the book, from the perspective of Helton's landmark contributions) -- Biographical Note and List of Publications of J.W. Helton -- Bounded Analytic Interpolation and H-infinity Control -- Linear Matrix Inequalities and Matrix Convexity -- Optimization and Realization in the Free *-algebra -- Automatic Verification of Matrix Inequalities -- Non-commutative Algebraic Geometry -- Non-Commutative Differential Geometry and Probability -- Modern Trends in Robust Control -- Challenges of Mathematical Biology -- Mathematical Programming and Computer Science.
Content:
This volume is dedicated to Bill Helton on the occasion of his sixty-fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control, and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty-odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, and as a source book for seminars.
Note:
Description based upon print version of record
,
Bill's Early WorkMike Crandall; Roger Howe; Ron Douglas; Joe; Backyard again; Thank You & Happy Birthday Bill; List of Contributors; Part II Technical Papers; The Carathéodory-Julia Theorem and the Network Realization Formula in Two Variables; 1. Introduction; 2. One variable realizations and models; 3. The Carath´eodory-Julia Theory in One Variable; 4. Two variable realizations and models; 5. The Carathéodory-Julia theorem in two variables; 6. Conclusion; References; Nevanlinna-Pick Interpolation via Graph Spaces and Krein-space Geometry: A Survey; 1. Introduction
,
2. The Sarason bitangential interpolation problem via the Grassmannian approach3. State-space realization of the J-Beurling-Lax representer; 3.1. A special case: left tangential operator-argument interpolation; 4. Extensions and generalizations of the Grassmannian method; 4.1. Interpolation problems for multipliers on the Drury-Arveson space; 4.2. Interpolation problems for multianalytic functions on the Fock space; References; A Brief History of the Strong Szegö Limit Theorem; 1. Introduction; 2. The precise version and sketch of the proof; 3. A Toeplitz determinant identity
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4. An application of Szegö's theorem5. Concluding remarks; References; Riccati or Square Root Equation? The Semi-separable Case; 1. Introduction; 2. Preliminaries; 3. System inversion: the Moore-Penrose case; 4. Constrained interpolation problems; 5.H∞-control for the semi-separable case; 6. Appendix: QR/QL/LQ/RQ factorization; References; Spectral Inclusion Theorems; 1. Introduction; 2. Gelfand theory; 3. Interpolating sequences and Berezin transforms; 4. Applications; References; Tutorial on a Nehari Problem and Related Reproducing Kernel Spaces; 1. Introduction
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2. Two reproducing kernel Hilbert spaces3. Some evaluations; 4. J spectral factorization; 5. The mvf Θ = GG+−1; 6. Detour on kernel formulas; 7. An alternate characterization of Θ; 8. Linear fractional transformations based on Θ; 9. The finite-dimensional Krein space KΘ; 10. Detour on J-inner mvf 's; References; Optimal Solutions to Matrix-valued Nehari Problems and Related Limit Theorems; 1. Introduction; 2. Restricted Nehari problems and relaxed commutant lifting; 3. Statement of the main convergence result; 4. The central optimal solution revisited; 5. The special case where M = Hp²
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6. Convergence of central optimal solutions
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Mathematical Methods in Systems, Optimization, and Control; Preface; Acknowledgement; Contents; Part I Biographical and Personal Notes; Helton's Bibliography; Personal Notes; After Dinner Biographical Notes; Basic Career Facts About Bill Helton; H∞ Engineering; Linear Matrix Inequalities vs Convexity; Other Areas that Bill Opened; Engineering vs Operator Model Theory vs Lax-Phillips Scattering; Noncommutative Geometry; Spectral Representations of Operators; Frequency Domain Optimization; Extending H∞ Control to Nonlinear Systems; Noncommutative Computer Algebra; Interdisciplinary Conferences
Additional Edition:
ISBN 9783034804103
Additional Edition:
Erscheint auch als Druck-Ausgabe Mathematical methods in systems, optimization, and control Basel : Birkhäuser, Springer, 2012 ISBN 9783034804103
Additional Edition:
ISBN 3034804105
Language:
English
Subjects:
Mathematics
Keywords:
Operatortheorie
;
Systemtheorie
;
Kontrolltheorie
;
Helton, J. William 1944-
;
Operatortheorie
;
Systemtheorie
;
Kontrolltheorie
;
Festschrift
;
Helton, J. William 1944-
;
Festschrift
DOI:
10.1007/978-3-0348-0411-0
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Putinar, Mihai 1955-
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