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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on classification of submodules in $H^{2}(D^{2})$
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by Rongwei Yang PDF
Proc. Amer. Math. Soc. 137 (2009), 2655-2659 Request permission

Abstract:

The Hardy spaces $H^{2}(D^{2})$ can be viewed as a module over the polynomial ring $C[z_1,z_2]$. Based on a study of core operator, a new equivalence relation for submodules, namely congruence, was introduced. This paper gives a classification of congruent submodules by the rank of core operators.
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Additional Information
  • Rongwei Yang
  • Affiliation: Department of Mathematics and Statistics, The State University of New York at Albany, Albany, New York 12222
  • Email: ryang@@math.albany.edu
  • Received by editor(s): September 9, 2008
  • Published electronically: March 30, 2009
  • Additional Notes: This work is supported in part by a grant from the National Science Foundation (DMS 0500333).
  • Communicated by: Nigel J. Kalton
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2655-2659
  • MSC (2000): Primary 47A13; Secondary 46E20
  • DOI: https://doi.org/10.1090/S0002-9939-09-09893-1
  • MathSciNet review: 2497478