Artículos de revistas
Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)
Registro en:
Symmetry Integrability And Geometry-methods And Applications. Natl Acad Sci Ukraine, Inst Math, v. 9, 2013.
1815-0659
WOS:000326493000001
10.3842/SIGMA.2013.065
Autor
Faustino, N
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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(-). 9 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) FCT (Portugal) through the European program COMPETE/FEDER [PTDC/MAT/114394/2009] Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) FAPESP [13/07590-8] FCT (Portugal) through the European program COMPETE/FEDER [PTDC/MAT/114394/2009]