عنوان

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

9783034885966

9783034896955

b406263

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

[Book]

edited by I. Gohberg.

Basel :

Imprint: Birkhäuser,

1992.

Operator Theory: Advances and Applications ;

58

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. Symbols discontinuous across a hyperplane in Rn x Rn -- References -- Program of Workshop.

0

9783034896955

Springer eBooks

Science (General).

Gohberg, I.

SpringerLink (Online service)

20190301080100.0

[Book]

Y