On some extension of Paley Wiener theorem
Paley Wiener theorem characterizes the class of functions which are Fourier transforms of ℂ∞ functions of compact support on ℝn by relating decay properties of those functions or distributions at infinity with analyticity of their Fourier transform. The theorem is already proved in classical case :...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-04-01
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| Series: | Concrete Operators |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/conop-2020-0006 |
| Summary: | Paley Wiener theorem characterizes the class of functions which are Fourier transforms of ℂ∞ functions of compact support on ℝn by relating decay properties of those functions or distributions at infinity with analyticity of their Fourier transform. The theorem is already proved in classical case : the real case with holomorphic Fourier transform on L2(ℝ), the case of functions with compact support on ℝn from Hörmander and the spherical transform on semi simple Lie groups with Gangolli theorem. |
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| ISSN: | 2299-3282 |