Convergence multipliers
From Encyclopedia of Mathematics
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
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