Carathéodory-Toeplitz and Nehari problems for matrix valued almost periodic functions

DOI10.1090/S0002-9947-98-01937-0zbMath0896.42005OpenAlexW1912194307MaRDI QIDQ4382354

Ilya M. Spitkovskij, Leiba Rodman, Hugo J. Woerdeman

Publication date: 30 March 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-01937-0

zbMATH Keywords

Fourier seriesNehari problemToeplitz operatorsHankel operatorsband methodBesicovitch spaceWiener algebracanonical factorizationpositive extensionsalmost periodic matrix functionCarathéodory-Toeplitz problemcontractive extensions

Mathematics Subject Classification ID

Classical almost periodic functions, mean periodic functions (42A75) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Linear operator methods in interpolation, moment and extension problems (47A57)

Related Items

Spectral factorization of bi-infinite multi-index block Toeplitz matrices ⋮ Factorization of matrix functions with subgroup supported Fourier coefficients ⋮ Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry ⋮ The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators ⋮ Non-denseness of factorable matrix functions ⋮ Toeplitz operators of finite interval type and the table method ⋮ Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications ⋮ The extension of positive definite operator-valued functions defined on a symmetric interval of an ordered group ⋮ Nehari and Carathéodory-Fejér type extension results for operator-valued functions on groups ⋮ Almost periodic factorization of certain block triangular matrix functions ⋮ Sarason interpolation and Toeplitz corona theorem for almost periodic matrix functions ⋮ Positive matrix functions on the bitorus with prescribed Fourier coefficients in a band ⋮ The spectral factorization problem for multivariable distributed parameter systems

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