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Sub Hilbert Spaces in a Bi-Disk

Published: 2 April 2013
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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.

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

Keywords

Hardy Space, Beurling Type Result, Isometry, Wold Type Decomposition

References
[1] A. Beurling, Two problems concerning linear transformations in Hilbert space, Acta Math. 81(1949), 239-255.
[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.
[11] D. Singh, Brangesian Spaces in the Polydisk, Proc. Amer. Math. Soc. 110(1990), 971-977.
[12] B. Yousefi and E. Hesameddini, Extension of the Beurling’s Theorem, Proc. Japan Acad. 84 (2008), 167-169.
Cite This Article
  • 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

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    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

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    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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  • @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}
    }
    

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    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
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  • Dept. of Mathematics

  • Dept. of Mathematics

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