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

AvI. Gohberg

Häftad, Engelska, 2012

Del 58 i serien Operator Theory: Advances and Applications

535 kr

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Produktinformation

Utgivningsdatum:2012-10-30
Mått:170 x 244 x 13 mm
Vikt:402 g
Format:Häftad
Språk:Engelska
Serie:Operator Theory: Advances and Applications
Antal sidor:214
Förlag:Springer Basel
ISBN:9783034896955

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Innehållsförteckning

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.- 2. Orthogonal operator-valued polynomials.- 3. Zeros of mat rix-valued Krein functions.- 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. Symbolsdiscontinuous across a hyperplane in Rn × Rn.- References.- Program of Workshop.