On convergence and divergence of Fourier expansions associated to Jacobi measure with mass points | Zendy

Bujar Xh. Fejzullahu | Zendy

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On convergence and divergence of Fourier expansions associated to Jacobi measure with mass points

Author(s) -

Bujar Xh. Fejzullahu

Publication year - 2009

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil0901061f

Subject(s) - mathematics , measure (data warehouse) , convergence (economics) , fourier series , divergence (linguistics) , lebesgue measure , fourier transform , pure mathematics , orthogonal polynomials , jacobi polynomials , lebesgue integration , mathematical analysis , linguistics , philosophy , database , computer science , economics , economic growth

We prove the failure of a.e. convergence of the Fourier expansion in terms of the orthonormal polynomials with respect to the measure (1 - x)α(1 + x)βdx + Mδ1 + Nδ1, where δt is the delta function at a point t and M > 0; N > 0: Lebesgue norms of Koornwinder's Jacobi-type polynomials are applied to obtain a new proof of necessary conditions for mean convergence. .

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