A study of Rhaly operators on Dirichlet series with real frequencies

In this thesis, we recall several important properties of the general Dirichlet series and characterize the entire Dirichlet series in the first two chapters. We also recall the Cesaro operator, an operator which was defined based on the Cesaro sum, and is heavily related to the Cesaro limits. A mor...

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Main Author: Koh, Ronald Joon Wei
Other Authors: Chua Chek Beng
Format: Theses and Dissertations
Language:English
Published: 2019
Subjects:
Online Access:https://hdl.handle.net/10356/82568
http://hdl.handle.net/10220/48148
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-825682023-02-28T23:53:52Z A study of Rhaly operators on Dirichlet series with real frequencies Koh, Ronald Joon Wei Chua Chek Beng Le Hai Khoi School of Physical and Mathematical Sciences DRNTU::Science::Mathematics In this thesis, we recall several important properties of the general Dirichlet series and characterize the entire Dirichlet series in the first two chapters. We also recall the Cesaro operator, an operator which was defined based on the Cesaro sum, and is heavily related to the Cesaro limits. A more general version of the Cesaro operator; Rhaly operators, will also be defined and the study of its properties on the Hilbert space of entire Dirichlet series is the bedrock of this thesis. Criterions will be provided for properties of Rhaly operators on the Hilbert space of entire Dirichlet series like boundedness and invariance. Compactness and Schatten p-class inclusions will also be studied on a smaller class of entire Dirichlet series; the small weighted Hilbert space of Dirichlet series. An additional section will also study injectivity and the closed range property of bounded Rhaly operators. Master of Science 2019-05-09T11:14:05Z 2019-12-06T14:58:07Z 2019-05-09T11:14:05Z 2019-12-06T14:58:07Z 2019 Thesis Koh, R. J. W. (2019). A study of Rhaly operators on Dirichlet series with real frequencies. Master's thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/82568 http://hdl.handle.net/10220/48148 10.32657/10220/48148 en 42 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle DRNTU::Science::Mathematics
Koh, Ronald Joon Wei
A study of Rhaly operators on Dirichlet series with real frequencies
description In this thesis, we recall several important properties of the general Dirichlet series and characterize the entire Dirichlet series in the first two chapters. We also recall the Cesaro operator, an operator which was defined based on the Cesaro sum, and is heavily related to the Cesaro limits. A more general version of the Cesaro operator; Rhaly operators, will also be defined and the study of its properties on the Hilbert space of entire Dirichlet series is the bedrock of this thesis. Criterions will be provided for properties of Rhaly operators on the Hilbert space of entire Dirichlet series like boundedness and invariance. Compactness and Schatten p-class inclusions will also be studied on a smaller class of entire Dirichlet series; the small weighted Hilbert space of Dirichlet series. An additional section will also study injectivity and the closed range property of bounded Rhaly operators.
author2 Chua Chek Beng
author_facet Chua Chek Beng
Koh, Ronald Joon Wei
format Theses and Dissertations
author Koh, Ronald Joon Wei
author_sort Koh, Ronald Joon Wei
title A study of Rhaly operators on Dirichlet series with real frequencies
title_short A study of Rhaly operators on Dirichlet series with real frequencies
title_full A study of Rhaly operators on Dirichlet series with real frequencies
title_fullStr A study of Rhaly operators on Dirichlet series with real frequencies
title_full_unstemmed A study of Rhaly operators on Dirichlet series with real frequencies
title_sort study of rhaly operators on dirichlet series with real frequencies
publishDate 2019
url https://hdl.handle.net/10356/82568
http://hdl.handle.net/10220/48148
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