On Convergence a Variation of the Converse of Fabry Gap Theorem

Molood Gorji; Naser Abbasi

doi:doi:10.11648/j.sjams.20150302.15

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On Convergence a Variation of the Converse of Fabry Gap Theorem

Molood Gorji, Naser Abbasi

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 2)

Received: 8 March 2015 Accepted: 26 March 2015 Published: 3 April 2015

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Abstract

In this article we give a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. whose circle of convergence is the unit circle and for which the unit circle is not the natural boundary.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 2)
DOI	10.11648/j.sjams.20150302.15
Page(s)	58-62
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Dirichlet Series, Entire Functions, Fabry Gap Theorem

References

[1]	Berenstein, C.A., and Gay Roger, Complex Analysis and Special Topics in Harmonic Analysis (New York, Inc: Springer-Verlag), (1995).
[2]	Blambert, M. and Parvatham, R., “Ultraconvergence et singualarites pour une classe de series d exponentielles.” Universite de Grenoble. Annales de l’Institut Fourier, 29(1), (1979), 239–262.
[3]	Blambert, M. and Parvatham, R., “Sur une inegalite fondamentale et les singualarites d une fonction analytique definie par un element LC-dirichletien. ” Universite de Grenoble. Annales de l’Institut Fourier, 33(4), (1983), 135–160.
[4]	Berland, M., “On the convergenve and singularities of analytic functions defined by E-Dirichletian elements. ” Annales des Sciences Mathematiques du Quebec, 22(1),(1998), 1–15.
[5]	Boas, R.P. Jr, , “Entire Functions,” (New York: Academic Press), (1954).
[6]	Erdos, P., “Note on the converse of Fabry's Gap theorem,” Trans. Amer. Math. Soc., 57, (1945), 102-104.
[7]	Polya, G., “On converse Gap theorems, ” Trans. Amer. Math. Soc., 52, (1942), 65-71.
[8]	Levin, B. Ya., “Distribution of Zeros of Entire Functions,” (Providence, R.I.: Amer. Math. Soc.), (1964).
[9]	Levin, B. Ya., “Lectures on Entire Functions, ” (Providence, R.I.: Amer. Math. Soc.), (1996).
[10]	Levinson, N., “Gap and Density Theorems. ” American Mathematical Society Colloquium Publications, Vol. 26 (New York: Amer. Math. Soc.), (1940).
[11]	Mandelbrojt, S., “Dirichlet Series, Principles and Methods,” (Dordrecht: D. Reidel Publishing Co.), (1972), pp. x‏166.
[12]	Zikkos, E., “On a theorem of Norman Levinson and a variation of the Fabry Gap theorem,” Complex Variables, 50 (4), (2005), 229-255.

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Molood Gorji, Naser Abbasi. (2015). On Convergence a Variation of the Converse of Fabry Gap Theorem. Science Journal of Applied Mathematics and Statistics, 3(2), 58-62. https://doi.org/10.11648/j.sjams.20150302.15

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ACS Style

Molood Gorji; Naser Abbasi. On Convergence a Variation of the Converse of Fabry Gap Theorem. Sci. J. Appl. Math. Stat. 2015, 3(2), 58-62. doi: 10.11648/j.sjams.20150302.15

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AMA Style

Molood Gorji, Naser Abbasi. On Convergence a Variation of the Converse of Fabry Gap Theorem. Sci J Appl Math Stat. 2015;3(2):58-62. doi: 10.11648/j.sjams.20150302.15

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@article{10.11648/j.sjams.20150302.15,
  author = {Molood Gorji and Naser Abbasi},
  title = {On Convergence a Variation of the Converse of Fabry Gap Theorem},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {2},
  pages = {58-62},
  doi = {10.11648/j.sjams.20150302.15},
  url = {https://doi.org/10.11648/j.sjams.20150302.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150302.15},
  abstract = {In this article we give a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. whose circle of convergence is the unit circle and for which the unit circle is not the natural boundary.},
 year = {2015}
}

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TY  - JOUR
T1  - On Convergence a Variation of the Converse of Fabry Gap Theorem
AU  - Molood Gorji
AU  - Naser Abbasi
Y1  - 2015/04/03
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150302.15
DO  - 10.11648/j.sjams.20150302.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 58
EP  - 62
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150302.15
AB  - In this article we give a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. whose circle of convergence is the unit circle and for which the unit circle is not the natural boundary.
VL  - 3
IS  - 2
ER  -

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Author Information

Molood Gorji

Department of Mathematics, Lorestan University, Khoramabad, Islamic Republic of Iran
Naser Abbasi

Department of Mathematics, Lorestan University, Khoramabad, Islamic Republic of Iran

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APA Style

Molood Gorji, Naser Abbasi. (2015). On Convergence a Variation of the Converse of Fabry Gap Theorem. Science Journal of Applied Mathematics and Statistics, 3(2), 58-62. https://doi.org/10.11648/j.sjams.20150302.15

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ACS Style

Molood Gorji; Naser Abbasi. On Convergence a Variation of the Converse of Fabry Gap Theorem. Sci. J. Appl. Math. Stat. 2015, 3(2), 58-62. doi: 10.11648/j.sjams.20150302.15

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AMA Style

Molood Gorji, Naser Abbasi. On Convergence a Variation of the Converse of Fabry Gap Theorem. Sci J Appl Math Stat. 2015;3(2):58-62. doi: 10.11648/j.sjams.20150302.15

Copy | Download

@article{10.11648/j.sjams.20150302.15,
  author = {Molood Gorji and Naser Abbasi},
  title = {On Convergence a Variation of the Converse of Fabry Gap Theorem},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {2},
  pages = {58-62},
  doi = {10.11648/j.sjams.20150302.15},
  url = {https://doi.org/10.11648/j.sjams.20150302.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150302.15},
  abstract = {In this article we give a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. whose circle of convergence is the unit circle and for which the unit circle is not the natural boundary.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - On Convergence a Variation of the Converse of Fabry Gap Theorem
AU  - Molood Gorji
AU  - Naser Abbasi
Y1  - 2015/04/03
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150302.15
DO  - 10.11648/j.sjams.20150302.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 58
EP  - 62
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150302.15
AB  - In this article we give a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. whose circle of convergence is the unit circle and for which the unit circle is not the natural boundary.
VL  - 3
IS  - 2
ER  -

Copy | Download