Our previous paper conducted to prove a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. In the present paper, we prove conversely convergence theorem of Fabry Gap. This is another proof of Fabry Gap theorem. This prove may be of interest in itself.
Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 4) |
DOI | 10.11648/j.sjams.20150304.12 |
Page(s) | 177-183 |
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. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Dirichlet Series, Entire Functions, Fabry Gap Theorem
[1] | Abbasi. N., Gorji, M., “On Convergence a Variation of the Converse of Fabry Gap Theorem, ” Science Journal of Applied Mathematics and Statistics, 3 (2), (2015), 58-62. |
[2] | Berenstein, C.A., and Gay Roger, “Complex Analysis and Special Topics in Harmonic Analysis” (New York, Inc: Springer-Verlag), (1995). |
[3] | 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. |
[4] | 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. |
[5] | 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. |
[6] | Boas, R.P. Jr, , “Entire Functions,” (New York: Academic Press), (1954). |
[7] | Erdos, P., “Note on the converse of Fabry's Gap theorem,” Trans. Amer. Math. Soc., 57, (1945), 102-104. |
[8] | Polya, G., “On converse Gap theorems, ” Trans. Amer. Math. Soc., 52, (1942), 65-71. |
[9] | Levin, B. Ya., “Distribution of Zeros of Entire Functions,” (Providence, R.I.: Amer. Math. Soc.), (1964). |
[10] | Levin, B. Ya., “Lectures on Entire Functions, ” (Providence, R.I.: Amer. Math. Soc.), (1996). |
[11] | Levinson, N., “Gap and Density Theorems. ” American Mathematical Society Colloquium Publications, Vol. 26 (New York: Amer. Math. Soc.), (1940). |
[12] | Mandelbrojt, S., “Dirichlet Series, Principles and Methods,” (Dordrecht: D. Reidel Publishing Co.), (1972), pp. x166. |
[13] | Valiron, M. G., “Sur les solutions des equations differentielles lineaires d'ordre infni et a coeffcients constants, ” Ann.Ecole Norm Trans, 3, 46, (1929), 25-53. |
[14] | Zikkos, E., “On a theorem of Norman Levinson and a variation of the Fabry Gap theorem,” Complex Variables, 50 (4), (2005), 229-255. |
APA Style
Naser Abbasi, Molood Gorji. (2015). Conversely Convergence Theorem of Fabry Gap. Science Journal of Applied Mathematics and Statistics, 3(4), 177-183. https://doi.org/10.11648/j.sjams.20150304.12
ACS Style
Naser Abbasi; Molood Gorji. Conversely Convergence Theorem of Fabry Gap. Sci. J. Appl. Math. Stat. 2015, 3(4), 177-183. doi: 10.11648/j.sjams.20150304.12
AMA Style
Naser Abbasi, Molood Gorji. Conversely Convergence Theorem of Fabry Gap. Sci J Appl Math Stat. 2015;3(4):177-183. doi: 10.11648/j.sjams.20150304.12
@article{10.11648/j.sjams.20150304.12, author = {Naser Abbasi and Molood Gorji}, title = {Conversely Convergence Theorem of Fabry Gap}, journal = {Science Journal of Applied Mathematics and Statistics}, volume = {3}, number = {4}, pages = {177-183}, doi = {10.11648/j.sjams.20150304.12}, url = {https://doi.org/10.11648/j.sjams.20150304.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150304.12}, abstract = {Our previous paper conducted to prove a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. In the present paper, we prove conversely convergence theorem of Fabry Gap. This is another proof of Fabry Gap theorem. This prove may be of interest in itself.}, year = {2015} }
TY - JOUR T1 - Conversely Convergence Theorem of Fabry Gap AU - Naser Abbasi AU - Molood Gorji Y1 - 2015/06/25 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150304.12 DO - 10.11648/j.sjams.20150304.12 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 - 177 EP - 183 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150304.12 AB - Our previous paper conducted to prove a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. In the present paper, we prove conversely convergence theorem of Fabry Gap. This is another proof of Fabry Gap theorem. This prove may be of interest in itself. VL - 3 IS - 4 ER -