Mean Convergence of Jacobi Series

Mean Convergence of Vector–valued Walsh Series

Given any Banach space X, let L X 2 denote the Banach space of all measurable functions f : [0, 1] → X for which f 2 := 1 0 f (t) 2 dt

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

The Mean Convergence of Orthogonal Series of Polynomials.

Mean and Almost Everywhere Convergence of Fourier-neumann Series

Let Jμ denote the Bessel function of order μ. The functions xJα+β+2n+1(x 1/2), n = 0, 1, 2, . . . , form an orthogonal system in L2((0,∞), xα+βdx) when α+ β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the Lp((0,∞), xαdx)-norm. Also, we describe the space in which the span of the system is dense and we show some of ...

Summability Method of Jacobi Series

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesàro (Λ · C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesàro method of Jacobi polynomials are estimated. The result of Theorem (6.1) of this research paper is applicable for avoiding the Gibbs phenomenon in intermediate levels of wavelet approximations. There are majo...