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Journal of Lie Theory 29 (2019), No. 3, 787--800
Copyright Heldermann Verlag 2019

A Local Levinson Theorem for Compact Symmetric Spaces

Mithun Bhowmik
Department of Mathematics, Indian Institute of Technology, Bombay, India

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the point-wise decay of their Fourier coefficients [Proc. London Math. Soc. (2), 41 (1936) 393--407]. We prove an analogue of this result on compact symmetric spaces.

Keywords: Riemannian symmetric space, Fourier transform, Levinson's theorem.

MSC: 43A85, 53C35, 33C55

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