The truncated Fourier operator. III
Victor Katsnelson, Ronny Machluf
TL;DR
This paper explores the spectral properties of the Fourier operator, detailing its eigenvectors, eigenspaces, and their mathematical structure, building on classical spectral theory and Hermite functions.
Contribution
It provides a detailed spectral analysis of the Fourier operator, including the construction of eigenvectors and eigenspaces, extending classical results with new insights.
Findings
Eigenvectors form a basis consisting of Hermite functions
Detailed description of eigenspaces in the spirit of Hardy and Titchmarsh
Spectral properties of the Fourier operator are elucidated
Abstract
The spectral theory of the Fourier operator (non-truncated) is expounded. The known construction of basis of eigenvectors consisting of the Hermite functions is presented. The detail description of the eigenspaces in the spirit of a work by Hardy and Titchmarsh is done.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · advanced mathematical theories · Material Science and Thermodynamics