Given a quadratic CR manifold M embedded in a complex space, we study Paley–Wiener–Schwartz theorems for spaces of Schwartz functions and tempered distributions on M. We discuss the interpretation of the space of restrictions of entire functions of exponential growth to M in terms of their non-commutative Fourier transform. We provide some structure results of the considered entire functions of exponential growth in terms of the geometric properties of M.
Paley–Wiener–Schwartz theorems on quadratic CR manifolds / M. Calzi. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 305:1(2023 Sep), pp. 8.1-8.35. [10.1007/s00209-023-03342-2]
Paley–Wiener–Schwartz theorems on quadratic CR manifolds
M. Calzi
2023
Abstract
Given a quadratic CR manifold M embedded in a complex space, we study Paley–Wiener–Schwartz theorems for spaces of Schwartz functions and tempered distributions on M. We discuss the interpretation of the space of restrictions of entire functions of exponential growth to M in terms of their non-commutative Fourier transform. We provide some structure results of the considered entire functions of exponential growth in terms of the geometric properties of M.
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