Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees

Article Type

Research Article

Publication Title

Analysis and Mathematical Physics

Abstract

In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability, growth estimate for functions in these spaces and their consequences. Equivalent conditions for multiplication operators to be bounded and compact are also obtained. Furthermore, we discuss about point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry.

First Page

267

Last Page

283

DOI

10.1007/s13324-016-0141-9

Publication Date

9-1-2017

Comments

Open Access, Green

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