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Topics in Operator Theory Volume 2: Systems and Mathematical Physics

:	Joseph A. Ball, Vladimir Bolotnikov, Leiba Rodman, Ilya M. Spitkovsky, J. William Helton
:	Joseph A. Ball, Vladimir Bolotnikov, J. William Helton, Leiba Rodman
:	Topics in Operator Theory Volume 2: Systems and Mathematical Physics
:	Birkhäuser Basel
:	9783034601610
:	1
:	CHF 133.00
:

:	Analysis
:	English

:	446
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

	Title Page	4
	Copyright Page	5
	Table of Contents	6
	The XIXth International Workshop on Operator Theory and its Applications. II	8
	Exact Solutions to the Nonlinear Schrodinger Equation	11
	1. Introduction	11
	2. Main results	14
	3. Examples	18
	References	21
	Robust Control, Multidimensional Systems and Multivariable Nevanlinna-Pick Interpolation	23
	1. Introduction	23
	2. The 1-D systems/single-variable case	28
	2.1. The model-matching problem	30
	2.2. The frequency-domain stabilization and H8 problem	30
	2.3. The state-space approach	32
	2.4. Notes	35
	3. The fractional representation approach to stabilizability and performance	35
	3.1. Parametrization of stabilizing controllers in terms of a given stabilizing controller	37
	3.2. The Youla-Kucera parametrization	41
	3.3. The standard H8-problem reduced to model matching.	45
	3.4. Notes	47
	4. Feedback control for linear time-invariant multidimensional systems	48
	4.1. Multivariable frequency-domain formulation	48
	4.2. Multidimensional state-space formulation	51
	4.3. Equivalence of frequency-domain and state-space formulations	62
	5. Robust control with structured uncertainty: the commutative case	68
	5.1. Gain-scheduling in state-space coordinates	69
	5.2. Gain-scheduling: a pure frequency-domain formulation	71
	5.3. Robust control with a hybrid frequency-domain/state-space formulation	71
	5.4. Notes	73
	6. Robust control with dynamic time-varying structured uncertainty	74
	6.1. The state-space LFT-model formulation	74
	6.2. A noncommutative frequency-domain formulation	79
	6.3. Equivalence of state-space noncommutative LFT-model and noncommutative frequency-domain formulation	84
	6.4. Notes	88
	References	90
	Absence of Existence and Uniqueness for Forward-backward Parabolic Equations on a Half-line	99
	1. Introduction	99
	2. Preliminaries	101
	3. Absence of existence and uniqueness	102
	4. Satisfaction of (C1)–(C4)	105
	References	107
	Bounds for Eigenvalues of the p-Laplacian with Weight Function of Bounded Variation	109
	1. Introduction	109
	2. Generalized total variation	111
	3. Estimates of eigenvalues	113
	4. Optimality of bounds I	116
	5. Optimality of bounds II	117
	6. The periodic p-Laplacian	120
	References	122
	The Gelfand-Levitan Theory for Strings	124
	1. Introduction	124
	2. Notation	127
	3. The spectral function .0,ß	128
	4. The transformation operator	131
	5. Existence of the transformation operator	134
	6. Smoothness	139
	7. The inverse problem	139
	8. The limit-point case	141
	9. The string	142
	References	144
	On the Uniqueness of a Solution to Anisotropic Maxwell’s Equations	146
	Introduction	146
	1. Basic boundary value problems for Maxwell’s equations	147
	2. A fundamental solution to Maxwell’s operator	153
	3. Green’s formulae	160
	4. Representation of solutions and layer potentials	162
	5. The uniqueness of a solution	165
	References	172
	Dichotomy and Boundedness of Solutions for Some Discrete Cauchy Problems	174
	1. Introduction	174
	2. Preliminary results	175
	3. Dichotomy and boundedness	177
	4. The case of operators acting on Banach spaces	180
	References	182
	Control Laws for Discrete Linear Repetitive Processes with Smoothed Previous Pass Dynamics	184
	1. Introduction	184
	2. Preliminaries and the new model	186
	3. Stability analysis	188
	4. Stabilization	191
	5. Robustness	193
	6. Numerical example	198
	7. Conclusions and further work	200
	References	201
	Fourier Method for One-dimensional Schrodinger Operators with Singular Periodic Potentials	203
	1. Introduction	203
	2. Preliminary results	206
	3. Fourier representation of the operators LPer±	221
	4. Fourier representation for the Hill–Schrodinger operator with Dirichlet boundary conditions	224
	5. Localization of spectra	230
	6. Conclusion	239
	References	241
	Additive Invariants on Quantum Channels and Regularized Minimum Entropy	245
	1. Introduction	245
	2. Proof of Theorem 1.1	247
	3. Examples	248
	4. Bi-quantum channels	251
	References	252
	A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators	254
	1. Introduction	254
	2. The functional model for indefinite Sturm-Liouville operators with one turning point	257
	2.1. Preliminaries	the functional model of a symmetric operator257
	2.2. The functional model for J-self-adjoint extensions of symmetric operators	258
	2.3. The Sturm-Liouville case	263
	3. Point and essential spectra of the model operator A and of indefinite Sturm-Liouville operators	267
	3.1. Point spectrum of the model operator	267
	3.2. Essential and discrete spectra of the model operator and of indefinite Sturm-Liouville operators	277
	3.3. Non-emptiness of resolvent set for Sturm-Liouville operators	279
	4. The absence of embedded eigenvalues and other applications	280
	4.1. The absence of embedded eigenvalues for the case of infinite-zone potentials	280
	4.2. Other applications	283
	5. Remarks on indefinite Sturm-Liouville operators with the singular critical point 0	284
	6. Discussion	286
	Appendix A. Boundary triplets for symmetric operators	289
	References	290