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Download Oleksiy Karlovych () De- partment of Mathematics, Escola de Ciencias, Universi-
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Oleksiy Karlovych ([email protected]) Department of Mathematics, Escola de Ciencias, Universidade do Minho, Campus de Gualtar, Braga, Portugal, Algebras of functions with Fourier coe¢ cients in Orlicz spaces and asymptotics of Toeplitz determinants. ABSTRACT. We consider a subset of the Wiener algebra consisiting of functions whose sequences of positive and negative Fourier coe¢ cients belong to weighted sequence Orlicz spaces. We prove that this set is a Banach algebra under pointwise multiplication and that every non-degenerating function from this algebra admits a Wiener-Hopf factorization. Using this result, we study asymptotics of the determinants of …nite Toeplitz matrices generated by functions from the above algebra and prove that the classical Szegö limit theorem is valid for these functions under natural assymptions. 1
