q-Extension of Mehta's eigenvectors of the finite Fourier transform forq, a root of unity

2008/11/30 by M. K. Atakishiyeva, Mesuma K. Atakishiyeva, Natig M. Atakishiyev +1
Computer Science · Mathematics · #Coding theory and cryptography #Computer science #Discrete Fourier transform (general) #Eigenvalues and eigenvectors #Extension (predicate logic) #Fourier analysis #Fourier series #Fourier transform #Fractional Fourier transform #Hermite polynomials #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Physics #Polynomial and algebraic computation #Pure mathematics #Quantum #Quantum mechanics #Root (linguistics) #Root of unity #Transformation (genetics) #math.CA #msc:33D45 #msc:42A38

paper · pdf · doi:10.1088/1751-8113/42/45/454004

published as J. Phys. A 42 (2009) 454004 · 12 pages, thoroughly rewritten, the q-extended eigenvectors now N-periodic with q an M-th root of 1

arxiv created 2009/05/21 · openalex publication_date 2009/10/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials. 2000MSC: 33D45, 42A38 1

Citations

• Linear Representations of Finite Groups
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Basic Hypergeometric Series
• Second Memoir on the Expansion of certain Infinite Products
• Is computing with the finite Fourier transform pure or applied mathematics?