Real Paley-Wiener theorems in spaces of ultradifferentiable functions

Abstract

We develop real Paley-Wiener theorems for classes ${\mathcal{S}}_{\omega }$ of ultradifferentiable functions and related $L^p$-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the so-called Gabor transform and give a full characterization in terms of Fourier and Wigner transforms for several variables of a Paley-Wiener theorem in this general setting, which is new in the literature. We also analyze this type of results when the support of the function is not compact using polynomials. Some examples are given.

References in corpus (5)

• Real Paley-Wiener theorems and local spectral radius formulas
• Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms
• A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions
• A characterization of the wave front set defined by the iterates of an operator with constant coefficients
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Cited by in corpus (4)

• About the nuclearity of ${\mathcal{S}}_{(M_p)}$ and ${\mathcal{S}}_{\omega }$
• Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
• Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis
• Compactness of localization operators on modulation spaces of $\omega$-tempered distributions