Applications of Berezin symbols in summability theory and related problems
Filomat, cilt.38, sa.12, ss.4355-4363, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 12
- Basım Tarihi: 2024
- Doi Numarası: 10.2298/fil2412355y
- Dergi Adı: Filomat
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.4355-4363
- Anahtar Kelimeler: Abel convergence, Berezin number, Berezin symbol, Borel convergence, Cesaro convergence, Radial limit, Reproducing kernel
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this article, using the reproducing kernel and Berezin symbol techniques we prove that a sequence is Cesàro convergent, then it is Abel convergent. We prove criteria for Borel convergence of some sequences and series of complex numbers. Also, we answer if the Berezin transform of a bounded operator on the Dirichlet space D and the Fock space F (Formula Presented) have radial limits almost everywhere. Moreover, we give an approximation problem for inner function by Berezin number of operators.