Abstract
We deal with single and double orthogonal series and give sufficient conditions which ensure their convergence almost everywhere. Among others, we prove that if ∑ ∞ j = 3 ∑ ∞ k = 3 a 2 jk log j log k log 2 + (1/ a 2 jk ) < ∞, then the series ∑ j ∑ k a jk ψ jk ( x) converges a.e. in Pringsheim′s sense for each double orthonormal system {ψ 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.