AN ESTIMATE TO FUNCTIONS WITH SECOND DERIVATIVES IN HOLDER CLASS BY MODULI OF CONTINUITY AND SOLUTION OF CHANDRASEKHAR'S WHITE DWARF EQUATION BY CHEBYSHEV WAVELET

AN ESTIMATE TO FUNCTIONS WITH SECOND DERIVATIVES IN HOLDER CLASS BY MODULI OF CONTINUITY AND SOLUTION OF CHANDRASEKHAR'S WHITE DWARF EQUATION BY CHEBYSHEV WAVELET

A. Aasma, P. N. Natarajan

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Abstract

We de ne the notion of absolute convergence with speed, where the speed is de ned by a monotonically increasing positive sequence  . Also we present the notion of absolute  -conservativity of a matrix, and the notion of improvement of  -convergence by a matrix. Let X; Y be two sequence spaces de ned by speeds of convergence. In this paper, we give necessary and su cient conditions for a matrix A (with real or complex entries) to map X into Y , if X or Y is the set of absolutely  -convergent sequences. We also present some examples of matrices being absolutely  -conservative or improving the absolute  -convergence, and consider these problems in the special cases if A is the Riesz matrix (R; pn) or the Zweier matrix Z1=2.

Keywords

Matrix transforms, convergence and absolute convergence with speed, absolute  -conservativity, improvement of  -convergence.