Intertwining operator associated to the complex Dunkl operator of type\n G(m,1,N)

2013/11/10 by Fethi Bouzeffour, Bouzeffour, Fethi, Sami Ghazouani +1
Mathematics · #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1311.2295

openalex publication_date 2013/11/10 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this work, we consider the Dunkl complex reflection operators related to\nthe group G(m,1,N) in the complex plane nT_i=
frac
partial
partial z_i+k₀
sum_j
neq\ni
sum_r=0^m-1
frac1-s_i^-r(i,j)s_i^r z_i-
varepsilon^r\nz_j+
sum_j=1^m-1k_j
sum_r=0^m-1
frac
varepsilon^-rjs_i^rz_i,\n
,
,1
leq i
leq N. We first review the theory of Dunkl operators\nfor complex reflection groups we recall some results related to the\nhyper--Bessel functions, which are solutions of a higher order differential\nequation. Secondly, we construct a new explicit intertwining operator between\nthe operator T_i and the partial derivative operator\n\(\∂)/(\∂ x_i). As application we given an explicit solution\nof the system: T_if(x)=
kappa
lambda_i f(x),
,
,
, f(0)=1.\n

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