Representations by Beurling Systems

Kazaros Kazarian ()
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Kazaros Kazarian: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Mod. 17, 28049 Madrid, Spain

Mathematics, 2023, vol. 11, issue 17, 1-17

Abstract: We prove that a Beurling system with F ∈ H p ( D ) , 1 ≤ p < ∞ is an M —basis in H p ( D ) with an explicit dual system. Any function f ∈ H p ( D ) , 1 ≤ p < ∞ can be expanded as a series by the system { z m F ( z ) } m = 0 ∞ . For different summation methods, we characterize the outer functions F for which the expansion with respect to the corresponding Beurling system converges to f . Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis.

Keywords: summation basis; hardy spaces; outer function; Beurling system; kernels; representation of functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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