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Gohberg I., Goldberg S., Kaashoek M. — Classes of linear operators. (volume 2)
Gohberg I., Goldberg S., Kaashoek M. — Classes of linear operators. (volume 2)

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Название: Classes of linear operators. (volume 2)

Авторы: Gohberg I., Goldberg S., Kaashoek M.

Аннотация:

This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering. Publication date: September 1993 Of interest to: Researchers, graduate students Codes: M16002, M16126, M16088, M16096 Classes of Linear Operators Vol. I This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. The present volume consists of four parts: general spectral theory, classes of compact operators, Fredholm and Wiener-Hopf operators, and classes of unbounded operators: The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 564

Добавлена в каталог: 16.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1$-solution      408
$C_0$ semigroup      415
a-invariant      326
Abstract Cauchy problem      408
Additive LU-decomposition      473 488
Adjoint boundary conditions      306
Adjoint in a *-algebra      906
Adjoint of an unbounded operator      290
Adjoint of differential operators      301 321 383
Adjoint, Lagrange adjoint      301 309 318
Algebra strongly decomposable      545
Algebra triangular      483
Algebra with band structure      905
Algebraic multiplicity of an eigenvalue for operator functions      205
Algebraic multiplicity of an eigenvalue for operators      26
Algebraic multiplicity of an eigenvalue, relative to a contour      205
Analytic at a point      6
Analytic on a set      6
Analytically matricially coupled      46
Approximately controllable      711
Approximately observable      710
Associated operator      54
Asymptotically stable, difference equation      58
Asymptotically stable, differential equation      20
Asymptotically stable, solution      20
Banach algebra      788
Banach algebra, commutative      788
Banach algebra, completion problems in a      939 943
Banach algebra, decomposing      806
Banach algebra, generated by      825
Banach algebra, identity of a      788
Banach algebra, semi-simple      828
Banach algebra, subalgebra of a      788
Banach algebra, unit of a      788
Banach algebra, unital      788
Band      906
Band completion      943
Band extension      908 943 955
Band matrix      897
Band matrix, m-band matrix      897
Band method      905
Bijection, associated with an operator      188
Blaschke factor      748
Block forward shift      656
Block Hankel operator      574
Block Laurent operator      564
Block Laurent operator, defined by      565
Block Laurent operator, defining function of      565
Block Toeplitz operator      561 570
Block Toeplitz operator, defined by      573
Block Toeplitz operator, defining function of      573
Boundary function      724
Boundary of class $C^2$      315
Bounded resolution of identity      72
Bounded variation      520
Brodski triangular integral      555
C*-algebra      843
Calkin algebra      191
Canonical factorization      235 588 832
Canonical realization      732
Caratheodory — Schur interpolation problem      692
Caratheodory — Toeplitz extension problem      949
Cascade connection      737 777
Cauchy contour      6
Cauchy domain      6
Cayley transform      346
Central extension      897 899
Central submatrix      897
Chain      473
Chain, associated with RHKS      499
Chain, closed      477
Chain, complement of      473
Chain, continuous      480
Chain, continuous function on      522
Chain, discontinuity of      474
Chain, finite      472
Chain, Hilbert space chain      476
Chain, integration along a      485
Chain, invariant      474
Chain, jump of      474
Chain, maximal      473 478
Chain, partition of      474
Chain, paxametrization of      480
Chain, rank of      556
Chain, reducing      474
Chain, refinement of      474
Chain, standard      473
Chain, uniform      475
Chain, unitarily equivalent      556
Characteristic operator function      717 781
Closable operator      289
Closed linear extension      289
Closed linear extension, minimal      289
Co-isometry      676
Coinciding operator functions      717
Commutant lifting theorem      685
Compact semigroup      435
Complete system of eigenvectors and generalized eigenvectors      135 378
Complete unitary invariant      713
Completely non-self adjoint      505
Completely non-unitary operator      700
Completely non-unitary semigroup      703
Completeness, problem of      29
Completion of a band      939 943
Completion of a band matrix      897
Completion of a lower triangular matrix      902
Completion, strictly contractive      917 946
Completion, triangular      948
Complex conjugation, closed under      845
Compression      666
Conjugate of an unbounded operator      292
Continuous function on a chain      522
Continuously differentiable solution      408
Contraction      665
Contraction semigroup      427
Contraction, strict      702
Contractive operator      665
Controllability gramian      970
Controllable      711
Controllable, approximately      711
Convolution operator with symbol      216
Coset      793
Coupling matrices      45
Coupling relation      45
Decomposing Banach algebra      806
Decomposing Banach algebra of continuous functions      837
Defect characteristic of an operator      773
Defect operator      665
Defining function of a block Laurent operator      565
Defining function of a block Toeplitz operator      573
Defining kernel      497
Derivative      7
Derivative, weak derivative      312
Determinant      114 804
Determinant, analyticity of      119
Diagonal in algebra with band structure      906
Diagonal left multiplicative      933
Diagonal right multiplicative      932 943
Diagonal with respect to a chain      474
Diagonal with respect to a finite chain      473
Differentiable      7
Differential operator      295 316 382 399
Differential operator on a half line      382
Differential operator, adjoint of      301 321 383
Differential operator, higher order      399
Differential operator, selfadjoint      341
Differential operator, uniformly elliptic      316
Dilation of an operator      667
Dilation of an operator function      696
Dilation of an operator function, minimal      696
Dilation of an operator, isometric      670
Dilation of an operator, minimal isometric      670
Dilation of an operator, minimal unitary      676
Dilation of an operator, N-step      673
Dilation of an operator, one step      673
Dilation of an operator, unitary      676
Direct sum of Hilbert spaces      657
Direct sum of operators on a Hilbert space      658
Dirichlet operator      316
Dirichlet operator, adjoint of      321
Dissipative operator on a Banach space      429
Dissipative operator on a Hilbert space      428
Dissipative, i-dissipative      506
Divergence form      316
Divisor of zero      796
Divisor of zero, topological      796
Domain, Cauchy domain      6
Domain, inner domain      49
Domain, outer domain      49
Douglas factorization lemma      680
Eigenvalue of an unbounded operator      349
Eigenvalue of finite type for a bounded operator      25
Eigenvalue of finite type for an operator function      205
Eigenvalue of finite type for an unbounded operator      326
Eigenvector of an unbounded operator      349
Eigenvector of an unbounded operator, generalized      378
Elementary Blaschke factor      748
Elementary pencil      747
Elementary rotation      748
Elementary solutions      29
Embedding of an operator into a system      716
Equivalence operator right      54 594
Equivalent, globally equivalent      38
Equivalent, locally equivalent      42
Equivalent, strictly equivalent      237
Essential spectrum for a bounded operator      191
Essential spectrum for an unbounded operator      373
Excessive subspace      707
Exponential representation      268
Exponential type zero      122
Extension $\mathcal{R}$-positive      908
Extension band      908 943 955
Extension central      897 899
Extension of a band matrix      897
Extension of a lower triangular matrix      902
Extension of an unbounded operator      290
Extension one-step      892
Extension positive      897
Extension problem of Caratheodory — Toeplitz      949
Extension problem of Nehari      957
Extension strictly contractive      902 917
Extension triangular      904 917 948 961
Extension Z-extension      38
Factorization canonical      235 588 597 832
Factorization indices      235 588 832
Factorization, determined by      746
Factorization, generalized LU      550
Factorization, left spectral      907
Factorization, left Wiener — Hopf      235 587
Factorization, LU      545
Factorization, regular      750
Factorization, right spectral      842 907
Factorization, right Wiener — Hopf      235 236 587 832
Factorization, spectral      842
Factorization, supported by      744
Factorization, Wiener — Hopf      234 585 587 832
Feedthrough operator      704
Final space of a partial isometry      84
Finite chain      472
Finite slab problem      274
Finitely meromorphic      206
First kind Wiener — Hopf operator      398
Fourier coefficients      562
Fourier series      563
Fourier transform      217 563 792
Fourier transformation      217 563 792
Fredholm operator, bounded      184
Fredholm operator, perturbation of      189 376
Fredholm operator, unbounded      372
Functional calculus      13 80 323
Functional model      733
Fundamental matrix      154
Gelfand representation      821
Gelfand spectrum      820
Gelfand topology      820
Gelfand transform      820
Gelfand — Mazur theorem      798
Gelfand — Naimark theorem      846
Generalized Dirichlet problem      316
Generalized eigenspace      30
Generalized eigenvectors      28 378
Generalized inverse      192
Generalized inverse in the weak sense      193
Generalized LU-factorization      550
Generalized resolvent equation      50
Generalized Wiener — Hopf equations      545
Generator of a semigroup      419
Geometric multiplicity      26
Globally equivalent      38
Gramian controllability      970
Gramian oberservability      970
Graph norm      369
Green’s formula      304
Green’s function      386
Half range problem      258
Hankel operator      225
Hankel operator, block      574
Hardy space      222 562
Hilbert space chain      476
Hilbert space direct sum of operators      658
Hilbert space direct sum of spaces      657
Hilbert — Schmidt norm      143
Hilbert — Schmidt operator      140
Hille — Yoshida — Phillips theorem      418
Homomorphism      821
Homomorphism, *-homorphism      847
i-dissipative      506
Ideal      793
Ideal, maximal      817
Ideal, proper      793
Identity of a Banach algebra      788
Index of a bounded Fredholm operator      184
Index of a bounded semi-Fredholm operator      283
Index of a unbounded Fredholm operator      372
Indicator      151
Infinitesimal generator of a semigroup      419
Initial space of a partial isometry      84
Inner domain      49
Inner function      660
input operator      704 776
Input space      704
Integral operator      148
Integral, along a chain      485
Integral, multiplicative      493
Interpolant, maximum entropy      971
Interpolant, strictly contractive      969
Interpolation problem, Carathedory — Schur      692
Interpolation problem, Nevanlinna — Pick      693 962 963
Interpolation problem, tangential Nevanlinna — Pick      965
Invariant projectionally      181
Invariant subspace      8
Invariant subspace theorem      478
Inverse      794
Invertible      794
Invertible, left      807
Involution      843
Isolated part of the spectrum      9
Isometric dilation      670
Isometric dilation, minimal      670
Isometric semigroup      431
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