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Non-harmonic cones are sets of injectivity for the twisted spherical means on $ \mathbb{C}^n$


Author: R. K. Srivastava
Journal: Trans. Amer. Math. Soc. 368 (2016), 1941-1957
MSC (2010): Primary 43A85; Secondary 44A35
DOI: https://doi.org/10.1090/tran/6488
Published electronically: June 18, 2015
MathSciNet review: 3449229
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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

DOI: https://doi.org/10.1090/tran/6488
Keywords: Heisenberg group, spherical harmonics, twisted convolution.
Received by editor(s): December 14, 2013
Received by editor(s) in revised form: January 11, 2014
Published electronically: June 18, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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