THEORY OF GENERALIZED HERMITE-POLYNOMIALS

We introduce multivariable generalized forms of Hermite polynomials an d analyze both the Gould-Hopper type polynomials and more general form s, which are analogues of the classical orthogonal polynomials, since they represent a basis ill L2(R(N)) Hilbert space, suitable for series expansion of square summable functions of N variables: Moreover, the role played by these generalized Hermite polynomials in the solution o f evolution-type differential equations is investigated: The key-note of the method leading to the multivariable polynomials is the introduc tion of particular generating functions, following the same criteria u nderlying the theory of multivariable generalized Bessel functions.