2013/03/12 by Hendrik De Bie, De Bie, Hendrik · 1 citation
Mathematics · Physics and Astronomy · #33C52 #42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.CA #math.MP #math.RT #msc:33C52 #msc:42B10
paper · pdf · doi:10.48550/arxiv.1303.2979
11 pages, various small changes, accepted for publication in Integral Transforms Spec. Funct
arxiv created 2013/04/29 · arxiv updated 2013/04/30
The radially deformed Fourier transform, introduced in [S. Ben Said, T. Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio Math.], is an integral transform that depends on a numerical parameter a ∈ R+. So far, only for a=1 and a=2 the kernel of this integral transform is determined explicitly. In the present paper, explicit formulas for the kernel of this transform are obtained when the dimension is even and a = 2/n with n ∈ N. As a consequence, it is shown that the integral kernel is bounded in dimension 2.