Abstract
We prove by means of the Berezin symbols some theorems for the $\left( L\right) $-summability method for sequences and series. Also, we prove a new Tauberian type theorem for $\left( L\right) $-summability.
Highlights
In this article, by applying a new functional analytic approach based on the so-called the Berezin symbol technique, we prove the following results
Recall that a sequencen≥0 of complex numbers an is said to be summable to a finite number ζ by the logarithmic method (L) (or (L) -summable to ζ ) if
The associated diagonal operator Da on H for any bounded sequencen≥0 of complex numbers is defined by the formula Daen (z) := anen (z), n = 0, 1, 2, ..., with respect to the orthonormal basis (en (z))n≥0 of H
Summary
By applying a new functional analytic approach based on the so-called the Berezin symbol technique, we prove the following results (see [3, 4]). We give a new Tauberian type theorem for (L) summable sequences of complex numbers. Recall that a sequence (an)n≥0 of complex numbers an is said to be summable to a finite number ζ by the logarithmic method (L) (or (L) -summable to ζ ) if
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
