On absolute convergence of Fourier integrals
E. Liflyand, R. Trigub
TL;DR
This paper establishes new sufficient conditions for representing functions as absolutely convergent Fourier integrals, focusing on the behavior of the function and its derivative at infinity, extended to higher dimensions.
Contribution
It introduces novel criteria involving the function and its derivative's behavior at infinity for absolute Fourier integral convergence, applicable in multiple dimensions.
Findings
New sufficient conditions for Fourier integral representation.
Extension of results to dimensions d ≥ 2.
Conditions involve behavior near infinity of functions and derivatives.
Abstract
New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Approximation Theory and Sequence Spaces