Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)

Autor(es)

Faustino, Nelson ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Matemat Aplicada, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Symmetry Integrability and Geometry-Methods and Applications; v. 9, 2013.
• Citações Web of Science: 4

Resumo

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(-). (AU)

• Processo FAPESP: 13/07590-8 - Aplicações de Cálculo de Clifford discreto em teorias de campos quânticos
• Beneficiário: Nelson José Rodrigues Faustino
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado