The eigenvectors of the discrete Fourier transform: A version of the Hermite functions

DOI10.1016/0022-247X(82)90199-8zbMath0516.65099WikidataQ56047060 ScholiaQ56047060MaRDI QIDQ1052814

F. Alberto Gruenbaum

Publication date: 1982

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

eigenvectorsdiscrete Fourier transformtridiagonal matrixHermite functionsmultiplicitiessimple spectrumcentered discrete Fourier transform

Mathematics Subject Classification ID

Trigonometric interpolation (42A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items

Explicit Hermite-type Eigenvectors of the Discrete Fourier Transform ⋮ The discrete fractional Fourier transform based on the DFT matrix ⋮ Efficient computation of DFT commuting matrices by a closed-form infinite order approximation to the second differentiation matrix ⋮ Discrete Fourier transform of prime order: eigenvectors with small support ⋮ Minimal Hermite-type eigenbasis of the discrete Fourier transform ⋮ On a Discrete Number Operator Associated with the 5D Discrete Fourier Transform ⋮ On eigenmeasures under Fourier transform ⋮ Eigenvectors of the discrete Fourier transform based on the bilinear transform ⋮ Chebyshev polynomials, Catalan numbers, and tridiagonal matrices ⋮ Topics on abelian spin models and related problems ⋮ The Heisenberg inequality for the discrete Fourier transform. ⋮ On supersymmetric eigenvectors of the 5D discrete Fourier transform ⋮ Discrete Fourier Transform and Extended Modified Hermite Polynomials ⋮ Three Theorems on Vandermond Matrices ⋮ On the diagonalization of the discrete Fourier transform ⋮ The compatibility dimension of quantum measurements ⋮ About two trigonometric matrices ⋮ Continuous vs. discrete fractional Fourier transforms ⋮ On eigenfunctions of continuous and discrete (anti)symmetric multivariate Fourier transforms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A remark on Hilber's matrix
• Analogues of Poisson's Summation Formula
• Is computing with the finite Fourier transform pure or applied mathematics?
• Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty-V: The Discrete Case