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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Non-harmonic cones are sets of injectivity for the twisted spherical means on $\mathbb {C}^n$
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by R. K. Srivastava PDF
Trans. Amer. Math. Soc. 368 (2016), 1941-1957 Request permission

Abstract:

In this article, we prove that a complex cone is a set of injectivity for the twisted spherical means for the class of all continuous functions on $\mathbb C^n$ as long as it does not completely lay on the level surface of any bi-graded homogeneous harmonic polynomial on $\mathbb C^n.$ Further, we produce examples of such level surfaces.
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Additional Information
  • R. K. Srivastava
  • Affiliation: Department of Mathematics, Indian Institute of Technology, Guwahati, India 781039
  • Email: rksri@iitg.ernet.in
  • Received by editor(s): December 14, 2013
  • Received by editor(s) in revised form: January 11, 2014
  • Published electronically: June 18, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1941-1957
  • MSC (2010): Primary 43A85; Secondary 44A35
  • DOI: https://doi.org/10.1090/tran/6488
  • MathSciNet review: 3449229