Ebook: Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton
- Tags: General Algebraic Systems, Control, Functions of a Complex Variable, Operator Theory, Operations Research Management Science
- Series: Operator Theory: Advances and Applications 222
- Year: 2012
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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, as well as a source book for seminars.
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, Szeg? 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.
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, Szeg? 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.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Helton’s Bibliography....Pages 3-12
Personal Notes....Pages 13-15
After Dinner Biographical Notes....Pages 17-21
Bill’s Early Work....Pages 23-28
List of Contributors....Pages 29-30
Front Matter....Pages 31-31
The Carath?odory-Julia Theorem and the Network Realization Formula in Two Variables....Pages 33-41
Nevanlinna-Pick Interpolation via Graph Spaces and Kre?n-space Geometry: A Survey....Pages 43-71
A Brief History of the Strong Szeg? Limit Theorem....Pages 73-83
Riccati or Square Root Equation? The Semi-separable Case....Pages 85-112
Spectral Inclusion Theorems....Pages 113-128
Tutorial on a Nehari Problem and Related Reproducing Kernel Spaces....Pages 129-149
Optimal Solutions to Matrix-valued Nehari Problems and Related Limit Theorems....Pages 151-172
On Theorems of Halmos and Roth....Pages 173-187
Pfister’s Theorem Fails in the Free Case....Pages 189-194
Free Analysis, Convexity and LMI Domains....Pages 195-219
Traces of Commutators of Integral Operators – the Aftermath....Pages 221-231
Information States in Control Theory: From Classical to Quantum....Pages 233-246
Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints....Pages 247-258
Computing Linear Matrix Representations of Helton-Vinnikov Curves....Pages 259-277
Positive Completion Problems Over C*-algebras....Pages 279-293
Front Matter....Pages 31-31
Fractional-order Systems and the Internal Model Principle....Pages 295-309
Optimal Mass Transport for Problems in Control, Statistical Estimation, and Image Analysis....Pages 311-324
LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future....Pages 325-349
Some Analysable Instances of ?-synthesis....Pages 351-368
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, Szeg? 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.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Helton’s Bibliography....Pages 3-12
Personal Notes....Pages 13-15
After Dinner Biographical Notes....Pages 17-21
Bill’s Early Work....Pages 23-28
List of Contributors....Pages 29-30
Front Matter....Pages 31-31
The Carath?odory-Julia Theorem and the Network Realization Formula in Two Variables....Pages 33-41
Nevanlinna-Pick Interpolation via Graph Spaces and Kre?n-space Geometry: A Survey....Pages 43-71
A Brief History of the Strong Szeg? Limit Theorem....Pages 73-83
Riccati or Square Root Equation? The Semi-separable Case....Pages 85-112
Spectral Inclusion Theorems....Pages 113-128
Tutorial on a Nehari Problem and Related Reproducing Kernel Spaces....Pages 129-149
Optimal Solutions to Matrix-valued Nehari Problems and Related Limit Theorems....Pages 151-172
On Theorems of Halmos and Roth....Pages 173-187
Pfister’s Theorem Fails in the Free Case....Pages 189-194
Free Analysis, Convexity and LMI Domains....Pages 195-219
Traces of Commutators of Integral Operators – the Aftermath....Pages 221-231
Information States in Control Theory: From Classical to Quantum....Pages 233-246
Convex Hulls of Quadratically Parameterized Sets With Quadratic Constraints....Pages 247-258
Computing Linear Matrix Representations of Helton-Vinnikov Curves....Pages 259-277
Positive Completion Problems Over C*-algebras....Pages 279-293
Front Matter....Pages 31-31
Fractional-order Systems and the Internal Model Principle....Pages 295-309
Optimal Mass Transport for Problems in Control, Statistical Estimation, and Image Analysis....Pages 311-324
LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future....Pages 325-349
Some Analysable Instances of ?-synthesis....Pages 351-368
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