Square summability with geometric weight for classical orthogonal expansions

Details Square summability with geometric weight for classical orthogonal expansions Square summability with geometric weight for classical orthogonal expansions

2006-04-03

arxiv.org/abs/math/0604028v1

Advances in Analysis, Proceedings of the 4th International ISAAC Conference (H. G. W. Begehr et al, eds.), World Scientific,

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

Let $f_k$ be the $k$-th Fourier coefficient of a function $f$ in terms of the orthonormal Hermite, Laguerre or Jacobi polynomials. We give necessary and sufficient conditions on $f$ for the inequality $\sum_{k}|f_k|^2\theta^k<\infty$ to hold with $\theta>1$. As a by-product new orthogonality relations for the Hermite and Laguerre polynomials are found. The basic machinery for the proofs is provided by the theory of reproducing kernel Hilbert spaces.

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