New Paley–Wiener Theorems

New Paley–Wiener Theorems

In this paper, for an arbitrary fixed compact set K , we find necessary and sufficient conditions on the Taylor expansion coefficients of entire functions of exponential type so that these functions are the Fourier image of distributions supported in K . In other words, we state the Paley–Wiener the...

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Veröffentlicht in:Complex analysis and operator theory 2020-06, Vol.14 (4), Article 47
Hauptverfasser: Bang, Ha Huy, Huy, Vu Nhat
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Entire functions
Higher Dimensional Geometric Function Theory and Hypercomplex Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Taylor series
Theorems
Thermal expansion
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Zusammenfassung:In this paper, for an arbitrary fixed compact set K , we find necessary and sufficient conditions on the Taylor expansion coefficients of entire functions of exponential type so that these functions are the Fourier image of distributions supported in K . In other words, we state the Paley–Wiener theorem in the language of Taylor expansion coefficients.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-020-01005-2