On the strong Cesaro summability of double orthogonal expansions

On the Restricted Cesaro Summability of Double Fourier Series

and po.biu, v), («, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ...

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Summability of orthogonal expansions of several variables

Square Summability with Geometric Weight for Classical Orthogonal Expansions

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 La...

On absolute matrix summability of orthogonal series

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...