Namespaces
Variants
Actions

Convergence multipliers

From Encyclopedia of Mathematics
Revision as of 17:11, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

for a series of functions

Numbers , such that the series converges almost-everywhere on a measurable set , where the are numerical functions defined on .

For example, for the trigonometric Fourier series of a function from , the numbers , are convergence multipliers ( and can be chosen arbitrarily), i.e. if and if

is its trigonometric Fourier series, then the series

converges almost-everywhere on the whole real line. If , , then its trigonometric Fourier series itself converges almost-everywhere (see Carleson theorem).

How to Cite This Entry:
Convergence multipliers. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_multipliers&oldid=32486
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article