On the maximum of the rectangular partial sums of double trigonometric series with nonnegative coefficients (Q1813772)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the maximum of the rectangular partial sums of double trigonometric series with nonnegative coefficients |
scientific article; zbMATH DE number 5059
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the maximum of the rectangular partial sums of double trigonometric series with nonnegative coefficients |
scientific article; zbMATH DE number 5059 |
Statements
On the maximum of the rectangular partial sums of double trigonometric series with nonnegative coefficients (English)
0 references
25 June 1992
0 references
The author proves a necessary and sufficient condition for integrability of the maximum of the partial sums of the double cosine and sine series with monotone coefficients as well as a sufficient one for pointwise and normwise convergence of these series. The results are two-dimensional analogues of a result of \textit{S. B. Stechkin} [Usp. Mat. Nauk 18, No. 1(109), 173--180 (1963; Zbl 0113.27502)], but which have been obtained in a different way.
0 references
double trigonometric series
0 references
double sine series
0 references
double cosine series
0 references
integrability
0 references
monotone coefficients
0 references
convergence
0 references
