Recently, Sahni and Singh [7] have solved an open problem posed by Yousefi and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables.
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 2) |
| DOI | 10.11648/j.pamj.20130202.17 |
| Page(s) | 98-100 |
| 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), 2013. Published by Science Publishing Group |
Hardy Space, Beurling Type Result, Isometry, Wold Type Decomposition
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| [2] | P.L. Duren, Theory of Hp spaces, Academic Press, Lon-don-New York, 1970. |
| [3] | K. Hoffman, Banach Spaces of Analytic Func- tions, Prentice Hall, Englewood Cliffs, New Jer- sey, 1962. |
| [4] | P. Koosis, Introduction to Hp spaces, Cambridge University Press, Cambridge, 1998. |
| [5] | V. Mandrakar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc., 1988, 145- 148. |
| [6] | D. A. Redett, Sub-Lebesgue Hilbert spaces on the unit circle, Bull. London Math. Soc. 37(2005), 793-800. |
| [7] | N. Sahni and D. Singh, Invariant subspaces of cer- tain sub-hilbert space of H2, Proc. Japan Acad., 87, Ser. A (2011), 56-59. |
| [8] | D. Sarason, Shift-Invariant spaces from the Bran- gesian point of view, The Bieberbach Conjecture, Mathematical Surveys and Monographs, AMS, 21(1986), 53-166. |
| [9] | H. S. Shapiro, Reproducing kernels and Beurling’s theorem, Trans. Amer. Math. Soc. 110 (1964), 448-458. |
| [10] | D. Singh and U.N. Singh, On a theorem of de Branges, Indian Journal of Math., 33(1991), 1- 5. |
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| [12] | B. Yousefi and E. Hesameddini, Extension of the Beurling’s Theorem, Proc. Japan Acad. 84 (2008), 167-169. |
APA Style
Niteesh Sahni, Niteesh Sahni. (2013). Sub Hilbert Spaces in a Bi-Disk. Pure and Applied Mathematics Journal, 2(2), 98-100. https://doi.org/10.11648/j.pamj.20130202.17
ACS Style
Niteesh Sahni; Niteesh Sahni. Sub Hilbert Spaces in a Bi-Disk. Pure Appl. Math. J. 2013, 2(2), 98-100. doi: 10.11648/j.pamj.20130202.17
AMA Style
Niteesh Sahni, Niteesh Sahni. Sub Hilbert Spaces in a Bi-Disk. Pure Appl Math J. 2013;2(2):98-100. doi: 10.11648/j.pamj.20130202.17
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Download@article{10.11648/j.pamj.20130202.17,
author = {Niteesh Sahni and Niteesh Sahni},
title = {Sub Hilbert Spaces in a Bi-Disk},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {2},
pages = {98-100},
doi = {10.11648/j.pamj.20130202.17},
url = {https://doi.org/10.11648/j.pamj.20130202.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.17},
abstract = {Recently, Sahni and Singh [7] have solved an open problem posed by Yousefi and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables.},
year = {2013}
}
TY - JOUR T1 - Sub Hilbert Spaces in a Bi-Disk AU - Niteesh Sahni AU - Niteesh Sahni Y1 - 2013/04/02 PY - 2013 N1 - https://doi.org/10.11648/j.pamj.20130202.17 DO - 10.11648/j.pamj.20130202.17 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 98 EP - 100 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20130202.17 AB - Recently, Sahni and Singh [7] have solved an open problem posed by Yousefi and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables. VL - 2 IS - 2 ER -
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