Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees
Functional Analysis
2016-08-12 v1
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.
Keywords
Cite
@article{arxiv.1608.03473,
title = {Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees},
author = {Perumal Muthukumar and Saminathan Ponnusamy},
journal= {arXiv preprint arXiv:1608.03473},
year = {2016}
}
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16 pages