Classes of linear operators
著者
書誌事項
Classes of linear operators
（Operator theory : advances and applications, v. 49,
Birkhäuser Verlag, 1990-1993
- v. 1 : sz
- v. 1 : us
- v. 2 : sz
- v. 2 : us
大学図書館所蔵 件 / 全45件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
-
v. 1 : sz ISBN 9783764325312
内容説明
After the book "Basic Operator Theory" by Gohberg-Goldberg was pub- lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex- pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in- stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol- umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.
目次
I. Riesz projections and functional calculus.- II. Eigenvalues of finite type.- III. Analytic equivalence.- IV. Linear operator pencils.- V. Spectral theory for bounded selfadjoint operators.- VI. Singular values of compact operators.- VII. Trace and determinant.- VIII. Hilbert-Schmidt operators.- IX. Integral operators with semi-separable kernels.- X. The growth of the resolvent operator and applications to completeness.- XI. Fredholm operators.- XII. Wiener-Hopf integral operators.- XIII. Wiener-Hopf integral operators with rational symbols.- XIV. Unbounded linear operators.- XV. Functional calculus for unbounded operators.- XVI. Unbounded selfadjoint operators.- XVII. Unbounded Fredholm operators and perturbation theorems.- XVIII. A class of ordinary differential operators on a half line.- XIX. Strongly continuous semigroups.- Standard references texts.- List of symbols.
- 巻冊次
-
v. 2 : sz ISBN 9783764329440
内容説明
This - book offers a panoptic view 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.
目次
Preface to Volume II. Table of contents of Volume II. Introduction. PART V: TRIANGULAR REPRESENTATIONS XX. Additive lower-upper triangular decompositions of operators 1. Additive lower-upper triangular decompositions relative to finite chains 2. Preliminaries about chains 3. Diagonals 4. Chains on Hilbert space 5. Triangular algebras 6. Riemann-Stieltjes integration along chains 7. Additive lower-upper decomposition theorem 8. Additive lower-upper decomposition of a Hilbert-Schmidt operator 9. Multiplicative integration along chains 10. Basic properties of reproducing kernel Hilbert spaces and chains 11. Example of an additive LU-decomposition in a RKHS. XXI. Operators in triangular form 1. Triangular representation 2. Intermezzo about completely nonselfadjoint operators 3. Volterra operators with a one-dimensional imaginary part 4. Unicellular operators. XXII. Multiplicative lower-upper triangular decompositions of operators 1. LU-factorization with respect to a finite chain 2. The LU-factorization theorem 3. LU-factorizations of compact perturbations of the identity 4. LU-factorizatioris of Hilbert-Schmidt perturbations of the identity 5. LU-factorizations of integral operators 6. Triangular representations of operators close to unitary 7. LU-factorization of semi-separable integral operators 8. Generalised Wiener-Hopf equations 9. Generalised LU-factorization relative to discrete chains. Comments on Part V Exercises to Part V PART VI: CLASSES OF TOEPLITZ OPERATORS XXIII. Block Toeplitz operators 1 Preliminaries 2. Block Laurent operators 3. Block Toeplitz operators 4. Block Toeplitz operators defined by continuous functions 5. The Fredholm index of a block Toeplitz operator defined by a continuous function. XXIV. Toeplitz operators defined by rational matrix functions 1. Preliminaries 2. Invertibility and Fredholm index (scalar case) 3. Wiener-Hopf factorization 4. Invertibility and Fredholm index (matrix case) 5. Intermezzo about realisation 6. Inversion of a block Laurent operator 7. Explicit canonical factorization 8. Explicit inversion formulas 9. Explicit formulas for Fredholm characteristics 10. An example 11. Asymptotic formulas for determinants of block Toeplitz matrices. XXV. Toeplitz operators defined by piecewise continuous matrix functions 1. Piecewise continuous functions 2. Symbol and Fredholm index (scalar case) 3. Symbol and Fredholm index (matrix case) 4. Sums of products of Toeplitz operators defined by piecewise continuous functions 5. Sums of products of block Toeplitz operators defined by piecewise continuous functions. Comments on Part VI. Exercises to Part VI. PART VII: CONTRACTIVE OPERATORS AND CHARACTERISTIC OPERATOR FUNCTIONS XXVI. Block shift operators 1. Forward shifts and isometries 2. Parts of block shift operators 3. Invariant subspaces of forward shift operators. XXVII. Dilation theory 1. Preliminaries about contractions 2. Preliminaries about dilations 3. Isometric dilations 4. Unitary dilations
「Nielsen BookData」 より