2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111418Let $f_k$ 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.11 pagesClassical Analysis and ODEs30B40, 46E22text