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

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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.

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Acknowledgments

The authors thank the referee for many useful comments which improve the presentation considerably. The first author thanks the Council of Scientific and Industrial Research (CSIR), India, for providing financial support in the form of a SPM Fellowship to carry out this research. The second author is on leave from the Indian Institute of Technology Madras, India.

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Authors and Affiliations

  1. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600 113, India

    Perumal Muthukumar & Saminathan Ponnusamy

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  1. Perumal Muthukumar
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  2. Saminathan Ponnusamy
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Correspondence to Saminathan Ponnusamy.

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Muthukumar, P., Ponnusamy, S. Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees. Anal.Math.Phys. 7, 267–283 (2017). https://doi.org/10.1007/s13324-016-0141-9

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  • DOI: https://doi.org/10.1007/s13324-016-0141-9

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