Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/72043
Type: Artigo de periódico
Title: Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)
Author: Faustino, N
Abstract: Based on the representation of a set of canonical operators on the lattice hZn, which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing su(1,1) symmetries. The Fourier decomposition of the space of Clifford-vector-valued polynomials with respect to the SO(n)Xsu(1,1)-module gives rise to the construction of new families of polynomial sequences as eigenfunctions of a coupled system involving forward/backward discretizations E+/-h of the Euler operator E=j=1nxjxj. Moreover, the interpretation of the one-parameter representation Eh(t)=exp(tE-h-tE+h) of the Lie group SU(1,1) as a semigroup (Eh(t))t=0 will allows us to describe the polynomial solutions of an homogeneous Cauchy problem on [0,8)XhZn involving the differencial-difference operator partial derivative(t)+E-h(+)-E-h(-).
Subject: Clifford algebras
finite difference operators
Lie algebras
Country: Ucrânia
Editor: Natl Acad Sci Ukraine, Inst Math
Rights: aberto
Identifier DOI: 10.3842/SIGMA.2013.065
Date Issue: 2013
Appears in Collections:Unicamp - Artigos e Outros Documentos

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