Square Summability with Geometric Weight for Classical Orthogonal Expansions
نویسنده
چکیده
Dmitrii Karp Institute of Applied Mathematics 7 Radio Street, Vladivostok, 690041, Russia [email protected] Abstra t Let fk be the k-th Fourier oe ient of a fun tion f in terms of the orthonormal Hermite, Laguerre or Ja obi polynomials. We give ne essary and su ient onditions on f for the inequality k |fk|θ < ∞ to hold with θ > 1. As a by-produ t new orthogonality relations for the Hermite and Laguerre polynomials are found. The basi ma hinery for the proofs is provided by the theory of reprodu ing kernel Hilbert spa es.
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