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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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1993Количество страниц: 564Добавлена в каталог: 16.06.2005Операции: Положить на полку |
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408 415 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 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 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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