Cím: | Almost everywhere convergence of orthogonal series revisited. |
Szerző: | M\'oricz, F.; Tandori, K. |
Forrás: | J. Math. Anal. Appl. 182, No.3, 637-653 (1994). |
Nyelv: | English |
Absztrakt: | We deal with single and double orthogonal series and give sufficient
conditions which ensure their convergence almost everywhere.
Among others, we prove that if $$\sum\sp \infty\sb{j= 3} \sum\sp
\infty\sb{k= 3} a\sb{jk}\sp 2\log j\log k\log\sp 2\sb +(1/a\sp
2\sb{jk})<\infty,$$ then the series $\sum\sb j\sum\sb k a\sb{jk}
\psi\sb{jk}(x)$ converges a.e. in Pringsheim's sense for each
double orthonormal system $\{\psi\sb{jk}(x)\}$. The interrelation
between the well-known Rademacher-Menshov (type) theorems and
ours are discussed in detail. At the end, we raise three problems
concerning the characterization of a.e. convergence of orthogonal
series. |
Letöltés: | | Zentralblatt |