On L-convergence of trigonometric series
Bogdan Szal
TL;DR
This paper investigates the conditions under which certain trigonometric series with specific coefficient properties converge in the L-norm, providing necessary and sufficient criteria based on the coefficients.
Contribution
It establishes new necessary and sufficient conditions for L-convergence of trigonometric series with (b,r)-general monotone and (b,r)-rest bounded variation coefficients.
Findings
Derived necessary and sufficient conditions for L-convergence.
Focused on series with (b,r)-general monotone coefficients.
Provided a comprehensive criterion in terms of coefficients.
Abstract
In the present paper we consider the trigonometric series with (b,r)-general monotone and (b,r)-rest bounded variation coefficients. Necessary and sufficien conditions of L-convergence for such series are obtained in terms of the coefficients.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research · Differential Equations and Boundary Problems