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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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 |
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DRNTU::Science::Mathematics Koh, Ronald Joon Wei A study of Rhaly operators on Dirichlet series with real frequencies |
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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 |
_version_ |
1759857140867006464 |