On a filter for exponentially localized kernels based on Jacobi polynomials |
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| Authors: | F Filbir HN Mhaskar J Prestin |
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| Institution: | aInstitute of Biomathematics and Biometry, Helmholtz Center Munich, 85764 Neuherberg, Germany;bDepartment of Mathematics, California State University, Los Angeles, CA 90032, USA;cInstitute of Mathematics, University of Lübeck, Wallstraße 40, 23560, Lübeck, Germany |
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| Abstract: | Let  , and for k=0,1,…,  denote the orthonormalized Jacobi polynomial of degree k. We discuss the construction of a matrix H so that there exist positive constants c, c1, depending only on H, α, and β such that Specializing to the case of Chebyshev polynomials,  , we apply this theory to obtain a construction of an exponentially localized polynomial basis for the corresponding L2 space. |
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| Keywords: | Spectral approximation Detection of analytic singularities Polynomial frames Filters and mollifiers Riesz basis |
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