Continuous and Discrete Fourier Transforms, Extension Problems and Wiener-Hopf Equations

Gohberg, Yisrael Z.:

ISBN 10: 3764328096 / ISBN 13: 9783764328092

Edité par Basel ; Boston ; Berlin : Birkhäuser, 1992

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VIII, 214 Pages Original Hardcover (Pappband) mit Bibliotheksschild auf Vorderdeckel. Innen mit Bibliotheksstempeln, sehr sauberes Exemplar. Englische Sprache. - Original Hardboard with Library label on front cover. Inside with Library stamps, in very good condition. English Language B15-03-02D|S99 Sprache: Englisch Gewicht in Gramm: 562 Operator Theory : Advances and Application ; Volume 58. N° de réf. du vendeur 62845

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Titre : Continuous and Discrete Fourier Transforms, ...

Éditeur : Basel ; Boston ; Berlin : Birkhäuser

Date d'édition : 1992

Reliure : 23,5 x 17 cm

Etat : Gut

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Synopsis :

Uncertainty principles for time-frequency operators.- 1. Introduction.- 2. Sampling results for time-frequency transformations.- 3. Uncertainty principles for exact Gabor and wavelet frames.- References.- Distribution of zeros of matrix-valued continuous analogues of orthogonal polynomials.- 1. Preliminary results.- 1.1. Matrix-valued Krein functions of the first and second kinds.- 1.2. Partitioned integral operators.- 2. Orthogonal operator-valued polynomials.- 2.1. Stein equations for operators.- 2.2. Zeros of orthogonal polynomials.- 2.3. On Toeplitz matrices with operator entries.- 3. Zeros of mat rix-valued Krein functions.- 3.1 On Wiener-Hopf operators.- 3.2. Proof of the main theorem.- References.- The band extension of the real line as a limit of discrete band extensions, II. The entropy principle.- 0. Introduction.- I. Preliminaries.- II. Main results.- References.- Weakly positive matrix measures, generalized Toeplitz forms, and their applications to Hankel and Hilbert transform operators.- 1. Lifting properties of generalized Toeplitz forms and weakly positive matrix measures.- 2. The GBT and the theorems of Helson-Szegö and Nehari.- 3. GNS construction, Wold decomposition and abstract lifting theorems.- 4. Multiparameter and n-conditional lifting theorems, the A-A-K theorem and applications in several variables.- References.- Reduction of the abstract four block problem to a Nehari problem.- 0. Introduction.- 1. Main theorems.- 2. Proofs of the main theorems.- References.- The state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols.- 1. Introduction and main theorems.- 2. Preliminaries on matrix pencils.- 3. Singular differential equations on the full-line.- 4. Singular differential equations on the half-line.- 5. Preliminaries on realizations.- 6. Proof of theorem 1.1.- 7. Proofs of theorems 1.2 and 1.3.- 8. An example.- References.- Symbols and asymptotic expansions.- 0. Introduction.- I. Smooth symbols on Rn.- II. Piecewise smooth symbols on T.- III. Piecewise smooth symbols on Rn.- IV. Symbols discontinuous across a hyperplane in Rn × Rn.- References.- Program of Workshop.