The truncated Fourier operator. II
Victor Katsnelson, Ronny Machluf
TL;DR
This paper investigates second-order differential operators that commute with the truncated Fourier operator on specific sets, enhancing understanding of their mathematical properties and potential applications.
Contribution
It identifies the simplest second-order differential operators commuting with the truncated Fourier operator for key sets, advancing spectral analysis in this area.
Findings
Characterization of differential operators commuting with _E
Explicit forms of these operators for different sets
Insights into spectral properties of _E
Abstract
For (E) being one of the three sets: the whole real axis, a finite symmetric interval and the positive semiaxis, we discuss the simplest differential operators of the second order which commute with the truncated Fourier operator (\mathscr{F}_E).
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Algebraic and Geometric Analysis · Nonlinear Waves and Solitons