Generalized hermite and laguerre polynomials and associated biorthogonal functions Biorthogonal sets and generalized polynomials

Generalized Hermite functions, with many variables and many indices, provide a set of biorthogonal functions whose importance in applications has been recently recognized. We remark on some of their properties, like those relevant to the Fourier-transform, and exploit them in order to introduce new classes of Laguerre polynomials along with the associated functions, whose properties are studied in detail.