arXiv math/06040282006-04-03math.CA

Square summability with geometric weight for classical orthogonal expansions

D. Karp

备注：: 11 pages
发表信息：: Advances in Analysis, Proceedings of the 4th International ISAAC Conference (H. G. W. Begehr et al, eds.), World Scientific, Singapore-NewJersey-London, 2005, 407-421

英文摘要：

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 $\sum_{k}|f_k|^2θ^k<\infty$ to hold with $θ>1$. 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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