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

InhaltsverzeichnisUncertainty 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.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.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.Reduction of the abstract four block problem to a Nehari problem.1. Main theorems.2. Proofs of the main theorems.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.Symbols and asymptotic expansions.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.Program of Workshop.