Real Paley-Wiener theorems in spaces of ultradifferentiable functions
نویسندگان
چکیده
منابع مشابه
Generalized Paley-Wiener Theorems
Non-harmonic Fourier transform is useful for the analysis of transient signals, where the integral kernel is from the boundary value of Möbius transform. In this note, we study the Paley–Wiener type extension theorems for the non-harmonic Fourier transform. Two extension theorems are established by using real variable techniques.
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The Fourier transforms of functions with compact and convex supports in R are described. The Fourier transforms of functions with nonconvex and unbounded supports are also considered.
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We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and prove three instances thereof, by using a reduction to the one-dimensional even case, shift operators, and a limit transition from Opdam’s results for the graded Hecke algebra, respectively. These Paley– Wiener theorems are used to extend Dunkl’s intertwining operator to arbitrary smooth functions. Furtherm...
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We prove a topological Paley-Wiener theorem for the Fourier transform deened on the real hyperbolic spaces SO o (p; q)=SO o (p ? 1; q), for p; q 2 2N, without restriction to K-types. We also obtain Paley-Wiener type theorems for L-Schwartz functions (0 < 2) for xed K-types.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2020
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2019.108348