دانلود کتاب Interpolation and realization theory with applications to control theory

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Contents......Page 6
Preface......Page 8
Visiting professorships......Page 10
Lectures at professional meetings......Page 11
Conference organization......Page 12
Memberships of professional organizations......Page 13
Papers in professional journals......Page 14
Papers published as book chapters......Page 23
Conference proceedings papers......Page 27
Edited books......Page 30
Ph.D. Students of J.A. Ball......Page 32
Quanlei Fang......Page 33
J. William Helton......Page 34
Sanne ter Horst......Page 35
Alexander Kheifets......Page 37
André Ran......Page 39
James Rovnyak......Page 40
1. Introduction......Page 42
2. The combined Nevanlinna–Schur class RS(M)......Page 48
3. Inner functions from the class RS(M)......Page 52
4. Characterization of the class RS(M)......Page 56
5. Compressed resolvents and the class N0m[–1,1]......Page 59
6. Transformations of the classes RS(M) and N0m[–1,1]......Page 60
B. Contractive 2 × 2 block operators......Page 80
References......Page 81
1. Introduction......Page 84
2. Proof of Proposition 1.3......Page 90
3. Proof of Theorem 1.1......Page 92
4. Examples......Page 95
4.1. A spectrahedron defined by a nilpotent tuple......Page 96
4.2. Bianalytic mappings of BE to a spectrahedron DB......Page 97
4.3.2. g = 2 type II algebra.......Page 98
References......Page 99
1. Introduction......Page 102
2. Proof of Theorem 1.3......Page 105
3. Toeplitz operators on U......Page 106
References......Page 110
1. Introduction......Page 112
2.1. LPU factorization......Page 115
2.2. On the role of complementarity......Page 116
2.3. One-sided factorability criteria......Page 118
2.4. Finite rank perturbations......Page 120
2.5. Triangular structure......Page 122
3.1. The problem......Page 124
3.2. Analysis of the problem......Page 126
3.3. Finite matrices......Page 130
3.4. Finite rank perturbations......Page 131
4.1. Reverse completion for T and T–1......Page 133
4.2. Block LU factorization......Page 134
References......Page 136
1. Introduction......Page 140
2. Schur class multipliers......Page 142
3. Polynomial vs. non-polynomial multipliers......Page 147
4. Corona theorem and spectral theory......Page 149
5. Commutators and localization......Page 150
6. Characterizations of multipliers......Page 152
References......Page 154
1. Introduction......Page 158
2. Row contractions and reproducing kernel Hilbert spaces......Page 160
3. Hardy space over the polydisc......Page 165
References......Page 170
1. Introduction......Page 173
2. Review and new results concerning Tω......Page 176
3. The spectrum of Tω......Page 180
4. The spectrum may be unbounded, the resolvent set empty......Page 182
5. The essential spectrum need not be connected......Page 184
6. A parametric example......Page 186
References......Page 193
1. Introduction......Page 195
2. General setting and main problem......Page 201
3. A numerical example and some illustrative special cases......Page 203
3.2. A class of finite-dimensional matrix examples......Page 204
3.3. Wiener algebra examples......Page 205
3.3.1. The Wiener algebra on the real line.......Page 206
3.3.2. The Wiener algebra on the unit circle.......Page 208
4. Preliminaries about Toeplitz-like and Hankel-like operators......Page 209
5. Further notations and auxiliary results......Page 211
6. An abstract inversion theorem......Page 217
7. Solution to the abstract twofold EG inverse problem......Page 220
8. Proof of Theorems 1.1 and 1.2......Page 223
8.1. Proof of Theorem 1.1......Page 224
8.2. Proof of Theorem 1.2......Page 230
9. The EG inverse problem with additional invertibility conditions......Page 233
10. Wiener algebra on the circle......Page 236
A.1. Preliminaries about Hankel operators......Page 241
A.2. Classical Hankel integral operators on L1 spaces......Page 243
A.3. Two auxiliary results......Page 248
References......Page 251
1.1. Data of the problem......Page 253
1.4. Special case......Page 254
2.1. The Nevanlinna–Pick interpolation problem......Page 255
2.2. The Sarason problem......Page 256
2.3. The boundary interpolation problem......Page 257
3.2. Unitary colligations, characteristic functions, Fourier representations......Page 259
3.3. Unitary extensions of the isometry V and solutions of the problem......Page 260
4.2. Universal extension of V......Page 261
4.3. Description of solutions......Page 262
5. Lecture 5: Inequality ║Fx║2 ≤ D(x,x), residual parts of minimal unitary extensions and the Nevanlinna–Adamjan– Arov–Kre.in type theorems......Page 263
5.2. Residual part of a minimal unitary extension and its spectral function......Page 264
5.3 Property ║Fx║2 ≤ D(x,x) yields boundary properties of the coefficient matrix S and the parameter ω......Page 267
6.1. The data of AIP suggest a dense set in HS......Page 269
6.2. Coefficient matrix of the Sarason problem and associated function model space......Page 270
6.3. Properties of the coefficient matrices of the Sarason problem......Page 271
References......Page 272
1. Introduction......Page 275
2. The tetrablock......Page 277
3. Realization formulae and the tetrablock......Page 278
4. The finite interpolation problem for Hol(D, ε)......Page 281
5. The structured singular value and the tetrablock......Page 283
References......Page 286
1. Introduction......Page 288
1.3. Overview......Page 292
2.1. Vector-valued RKHS......Page 293
2.2. Herglotz spaces......Page 295
2.4. Gleason solutions......Page 297
2.10. Extremal Gleason solutions......Page 299
2.16. de Branges–Rovnyak model via transfer-function theory......Page 301
3. Completely non-coisometric row contractions......Page 303
4. Model maps for CCNC row partial isometries......Page 312
4.17. The characteristic function is not a complete unitary invariant......Page 320
4.22. Frostman shifts......Page 322
5.1. Automorphisms of the unit ball of L(H, K)......Page 325
5.3. Frostman shifts of Schur functions......Page 327
5.9. Gleason solution model for CCNC row contractions......Page 331
6.1. Quasi-extreme Schur multipliers......Page 335
6.7. de Branges–Rovnyak model for quasi-extreme row contractions......Page 339
7. Outlook......Page 341
References......Page 342
1. Introduction......Page 345
2. Numerical scheme for computing rk and pk......Page 350
2.1. Rational function approximation and partial fraction decomposition......Page 351
2.2. Two-sided residue interpolation in the Stieltjes class......Page 352
3. Numerical examples......Page 354
4. Conclusions......Page 360
References......Page 364
1. Introduction......Page 367
2. Preliminaries about graphs......Page 368
3. Resistive electrical networks......Page 369
4.1. Kirchhoff’s problem......Page 371
4.2. The dual problem......Page 373
4.4. The prescribed power problem......Page 374
5. The discrete version of Calder´on’s inverse problem......Page 375
7. Conclusions......Page 377
References......Page 378
1. Introduction......Page 380
2. Lotka–Volterra and radiotherapy......Page 381
2.1. Analysis of system......Page 382
2.2. Case I: cancer always wins without control......Page 383
2.3. Case II: if tumor sufficiently shrinks, it is eliminated by the body......Page 384
3. Norton–Massagu´e dynamics: system identification and control......Page 385
3.3. Numerical example......Page 388
4. Conclusions......Page 389
References......Page 390