DISCRETE FOURIER TRANSFORM ASSOCIATED WITH GENERALIZED SCHUR POLYNOMIALS

被引：9

作者：

van Diejen, J. F. ^{[1
]}

Emsiz, E. ^{[2
]}

机构：

[1] Univ Talca, Inst Matemat & Fis, Casilla 747, Talca, Chile

[2] Pontificia Univ Catolica Chile, Fac Matemat, Casilla 306,Correo 22, Santiago, Chile

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 08期

关键词：

Discrete Fourier transform; discrete Laplacian; boundary perturbations; diagonalization; generalized Schur polynomials; ORTHOGONAL POLYNOMIALS; MODEL;

D O I：

10.1090/proc/14036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this recovers the sixteen classic discrete sine-and cosine transforms DST-1, ... , DST-8 and DCT-1, ... , DCT-8, as well as recently studied (anti) symmetric multivariate generalizations thereof.

引用

页码：3459 / 3472

页数：14

共 50 条

[1] Discrete Fourier Transform and Extended Modified Hermite Polynomials
Malekar, R. A.
MATHEMATICAL ANALYSIS AND ITS APPLICATIONS, 2015, 143 : 557 - 563
[2] Generalized Discrete Fourier Transform With Nonlinear Phase
Akansu, Ali N.
Agirman-Tosun, Handan
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2010, 58 (09) : 4547 - 4556
[3] Generalized Discrete Fourier Transform: Theory and Design Methods
Akansu, Ali N.
Agirman-Tosun, Handan
2009 IEEE SARNOFF SYMPOSIUM, CONFERENCE PROCEEDINGS, 2009, : 551 - 557
[4] Computing Zernike polynomials of arbitrary degree using the discrete Fourier transform
Janssen, Augustus J. E. M.
Dirksen, Peter
JOURNAL OF THE EUROPEAN OPTICAL SOCIETY-RAPID PUBLICATIONS, 2007, 2
[5] A discrete Fourier transform associated with the affine Hecke algebra
van Diejen, J. F.
Emsiz, E.
ADVANCES IN APPLIED MATHEMATICS, 2012, 49 (01) : 24 - 38
[6] On the generalized Fourier transform
Abreu-Blaya, Ricardo
Rodriguez, Jose M.
Sigarreta, Jose M.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (16) : 16709 - 16733
[7] On a Discrete Number Operator Associated with the 5D Discrete Fourier Transform
Atakishiyeva, M. K.
Atakishiyev, N. M.
Mendez Franco, J.
DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS, ICDDEA 2015, 2016, 164 : 273 - 292
[8] THE FINITE FOURIER TRANSFORM OF CLASSICAL POLYNOMIALS
Dixit, Atul
Jiu, Lin
Moll, Victor H.
Vignat, Christophe
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 98 (02) : 145 - 160
[9] Uniqueness of the discrete Fourier transform
Baraquin, Isabelle
Ratier, Nicolas
SIGNAL PROCESSING, 2023, 209
[10] On the diagonalization of the discrete Fourier transform
Gurevich, Shamgar
Hadani, Ronny
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2009, 27 (01) : 87 - 99

← 1 2 3 4 5 →