This article is cited in 16 papers

Duhamel Algebras and Applications

M. T. Karaev<sup>ab

a</sup> Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
^b Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia

Abstract: We introduce Duhamel algebras and study their properties and applications. We prove that a Banach space of analytic functions on the unit disc that satisfy certain conditions is a Duhamel algebra and describe its closed ideals. These results substantially generalize and improve the main results of Wigley's papers. Some other related questions are also discussed.

Keywords: Duhamel algebra, closed ideal, Hardy space, Banach space of analytic functions, invariant subspace.

UDC: 917.98+512.55

Received: 13.05.2016

DOI: 10.4213/faa3481

 English version: Functional Analysis and Its Applications, 2018, 52:1, 1–8

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