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Strong summability of Riesz means. (English. Russian original) Zbl 0656.42016
Math. Notes 40, 706-713 (1986); translation from Mat Zametki 40, No. 3, 352-363 (1986).
Let $$\{u_ n(x)\}$$ be a complete orthonormalized system of eigenfunctions of the self-adjoint extension of Laplace operator - $$\Delta$$ in N-dimensional domain $$\Omega$$ with discrete spectrum, and let $$\lambda_ n=\mu_ n^ 2$$ be the corresponding eigenvalues numbered in increasing order. We consider the Riesz mean of order $$s\geq 0$$ of the Fourier series with respect to system $$\{u_ n(x)\}$$ of function f(x) of $$L_ 2(\Omega):$$ $\sigma^{s}_{\mu}(f,x)=\sum_{\mu_ n<\mu}(1- \frac{\mu^ 2_ n}{\mu^ 2})^ sf_ nu_ n(x).$ We find the de la Vallée-Poussin sums of the Riesz means of function f(x).
##### MSC:
 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
##### Keywords:
Laplace operator; de la Vallée-Poussin; Riesz means
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##### References:
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