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THE WEYL TRANSFORM OF A SMOOTH MEASURE ON A REAL-ANALYTIC SUBMANIFOLD

Part of: Lie groups Locally compact groups and their algebras Symplectic geometry, contact geometry Abstract harmonic analysis

Published online by Cambridge University Press:  11 October 2024

MANSI MISHRA Open the ORCID record for MANSI MISHRA [Opens in a new window]  and
M. K. VEMURI Open the ORCID record for M. K. VEMURI [Opens in a new window]
MANSI MISHRA*
Affiliation:
Department of Mathematical Sciences, IIT(BHU), Varanasi, 221005, India
M. K. VEMURI
Affiliation:
Department of Mathematical Sciences, IIT(BHU), Varanasi, 221005, India e-mail: mkvemuri.mat@itbhu.ac.in
*
e-mail: mansimishra.rs.mat19@itbhu.ac.in
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Abstract

If $\mu $ is a smooth measure supported on a real-analytic submanifold of ${\mathbb {R}}^{2n}$ which is not contained in any affine hyperplane, then the Weyl transform of $\mu $ is a compact operator.

Keywords

absolute continuitycompact operatorreal-analytic submanifoldtwisted convolution

MSC classification

Primary: 43A10: Measure algebras on groups, semigroups, etc.
Secondary: 22D10: Unitary representations of locally compact groups 22E30: Analysis on real and complex Lie groups 43A80: Analysis on other specific Lie groups 53D55: Deformation quantization, star products

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 112 , Issue 1 , August 2025 , pp. 184 - 193
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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