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DISCRETE WIENER-HOPF OPERATORS ON ORLICZ SEQUENCE SPACES

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Resumo:Given a function (called a symbol) with Fourier coefficients ( )∈Z, the associated discrete Wiener-Hopf operator () acts on the sequence = ( )∈{0,1,2,... } by (() ) = ∞Õ =0 − , ∈ {0, 1, 2, . . . }. An operator is said to be Fredholm if it has a finite dimensional kernel and cokernel. The study of Fredholm properties of Wiener-Hopf operators plays a fundamental role in operator theory and has been extensively developed in the classical Lebesgue space setting. In this thesis, we develop a Fredholm theory for discrete Wiener-Hopf operators acting on reflexive Orlicz sequence spaces. The main objective is to characterize the Fredholm property in terms of the associated symbols under suitable assumptions, extending several classical results from Lebesgue sequence space settings to the more general framework of Orlicz sequence spaces. We introduce a Banach algebra of multipliers and investigate the Fredholm properties of the associated operators. In particular, several important subalgebras of the multiplier algebra are considered, including those consisting of continuous symbols, symbols be- longing to Douglas-type algebras, and piecewise continuous symbols. For continuous symbols and symbols in Douglas-type algebras, necessary and sufficient conditions for Fredholmness are established, while for piecewise continuous symbols a sufficient con- dition is obtained. The analysis relies on a combination of Banach algebra techniques, localization methods and interpolation tools adapted to Orlicz sequence spaces. The Fredholm theory is further extended to the algebras generated by discrete Wiener- Hopf operators with symbols in the above algebras. In addition, the results are generalized to matrix-valued symbols, and Fredholm criteria are established for the corresponding matrix-valued operators.
Autores principais:Thampi, Sandra Mary
Assunto:discrete Wiener-Hopf operators Orlicz sequence spaces Fredholm theory Matuszewska-Orlicz indices periodic distributions
Ano:2026
País:Portugal
Tipo de documento:tese de doutoramento
Tipo de acesso:acesso aberto
Instituição associada:Universidade Nova de Lisboa
Idioma:inglês
Origem:Repositório Institucional da UNL

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