Algebra of entire Dirichlet series with real frequencies
We study the class E(Λ,C) of all entire Dirichlet series with real frequencies Λ (which are generalizations of classical Dirichlet series as well as power series). Our method, based on Number Theory, allows us to get a link between the set of real frequencies and the set of counting numbers. So the...
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sg-ntu-dr.10356-1434432023-02-28T19:39:12Z Algebra of entire Dirichlet series with real frequencies Jeck, Lim Khoi, Le Hai School of Physical and Mathematical Sciences Science::Mathematics Hilbert Space Entire Dirichlet Series with Real Frequencies We study the class E(Λ,C) of all entire Dirichlet series with real frequencies Λ (which are generalizations of classical Dirichlet series as well as power series). Our method, based on Number Theory, allows us to get a link between the set of real frequencies and the set of counting numbers. So the following problems posed by C.O. Kiselman have been solved: (i) the criteria for E(Λ,C) to be closed (invariant) under multiplication; (ii) the explicit description of the smallest subalgebra of entire functions that contains E(Λ,C). Some open questions are provided. Ministry of Education (MOE) Accepted version Supported in part by MOE’s AcRF Tier 1 grant M4011724.110 (RG128/16). 2020-09-02T01:01:20Z 2020-09-02T01:01:20Z 2018 Journal Article Jeck, L., & Khoi, L. H. (2019). Algebra of entire Dirichlet series with real frequencies. Complex Variables and Elliptic Equations, 65(2), 229-244. doi:10.1080/17476933.2019.1579204 1747-6933 https://hdl.handle.net/10356/143443 10.1080/17476933.2019.1579204 2-s2.0-85063914592 2 65 229 244 en Complex Variables and Elliptic Equations This is an Accepted Manuscript of an article published by Taylor & Francis in Complex Variables and Elliptic Equations on 04 April 2019, available online: http://www.tandfonline.com/10.1080/17476933.2019.1579204. application/pdf |
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Science::Mathematics Hilbert Space Entire Dirichlet Series with Real Frequencies Jeck, Lim Khoi, Le Hai Algebra of entire Dirichlet series with real frequencies |
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We study the class E(Λ,C) of all entire Dirichlet series with real frequencies Λ (which are generalizations of classical Dirichlet series as well as power series). Our method, based on Number Theory, allows us to get a link between the set of real frequencies and the set of counting numbers. So the following problems posed by C.O. Kiselman have been solved: (i) the criteria for E(Λ,C) to be closed (invariant) under multiplication; (ii) the explicit description of the smallest subalgebra of entire functions that contains E(Λ,C). Some open questions are provided. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Jeck, Lim Khoi, Le Hai |
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Article |
author |
Jeck, Lim Khoi, Le Hai |
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Jeck, Lim |
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Algebra of entire Dirichlet series with real frequencies |
title_short |
Algebra of entire Dirichlet series with real frequencies |
title_full |
Algebra of entire Dirichlet series with real frequencies |
title_fullStr |
Algebra of entire Dirichlet series with real frequencies |
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Algebra of entire Dirichlet series with real frequencies |
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algebra of entire dirichlet series with real frequencies |
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2020 |
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https://hdl.handle.net/10356/143443 |
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