Positivity of the Jacobi-Cherednik intertwining operator and its dual

被引：31

作者：

Gallardo, Leonard ^{[1
]}

Trimeche, Khalifa ^{[2
]}

机构：

[1] Univ Tours, CNRS, Lab Math & Phys Theor, UMR 6083, Campus Grandmont, F-37200 Tours, France

[2] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

ADVANCES IN PURE AND APPLIED MATHEMATICS | 2010年 / 1卷 / 02期

关键词：

Jacobi-Cherednik operator; intertwining operator; Laplace formula for the eigenfunctions; positivity of the intertwining kernel; intertwining dual operator;

D O I：

10.1515/APAM.2010.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to the study of the differential-difference Jacobi-Cherednik operator defined for f is an element of C-1(R) by T-(k,T- k') f(x) = f'(x) + (k coth(x) + k' tanh (x))(f(x) - f(-x)) - (k + k') f(-x), where k > 0 and k' >= 0 are two parameters, and to the positivity of the operator which intertwines T-(k,T- (k')) and the derivative operator d/dx.

引用

页码：163 / 194

页数：32

共 16 条

[1] A UNIFICATION OF KNIZHNIK-ZAMOLODCHIKOV AND DUNKL OPERATORS VIA AFFINE HECKE ALGEBRAS [J].

CHEREDNIK, I .

INVENTIONES MATHEMATICAE, 1991, 106 (02) :411-431

[2] POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON R [J].

Chouchane, F. ;

Mili, M. ;

Trimeche, K. .

ANALYSIS AND APPLICATIONS, 2003, 1 (04) :387-412

[3] INTEGRAL-KERNELS WITH REFLECTION GROUP INVARIANCE [J].

DUNKL, CF .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1991, 43 (06) :1213-1227

[4]

Erdelyi A., 1953, HIGHER TRANSCENDENTA

[5]

Gradshteyn I. S., 2014, TABLE INTEGRALS SERI

[6]

HECKMAN GJ, 1987, COMPOS MATH, V64, P329

[7]

Heckmann G. J., 1994, HARMONIC ANAL SPECIA

[8] NEW PROOF OF A PALEY-WIENER TYPE THEOREM FOR JACOBI TRANSFORM [J].

KOORNWINDER, T .

ARKIV FOR MATEMATIK, 1975, 13 (01) :145-159

[9]

Koornwinder T.H., 1984, SPECIAL FUNCTIONS GR

[10] TRANSMUTATION OPERATORS AND PALEY-WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE [J].

Mourou, Mohamed A. ;

Trimeche, Khalifa .

ANALYSIS AND APPLICATIONS, 2003, 1 (01) :43-70

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