Cesàro summability of Taylor series in higher order weighted Dirichlet-type spaces

• Autorzy: Ghara Soumitra , Gupta Rajeev , Reza Md. Ramiz

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.373

• Języki publikacji: EN

Abstrakty

EN

For a positive integer m and a finite non-negative Borel measure μ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces Hμ,m. We show that if [formula], then for any f in Hμ,m, the sequence of generalized Cesàro sums [formula] converges to f. We further show that if [formula] then for the Dirac delta measure supported at any point on the unit circle, the previous statement breaks down for every positive integer m.

Słowa kluczowe

EN

weighted Dirichlet-type integrals; Cesàro means; summability; Hadamard multiplication

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 373--390
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Ghara Soumitra

• Department of Mathematics, Indian Institute of Technology Kharagpur, Midnapore - 721302, India

autor

Gupta Rajeev

• School of Mathematics and Computer Science, Indian Institute of Technology Goa, Goa - 403401, India

autor

Reza Md. Ramiz

• School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala - 695551, India

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)