This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator cal...

This paper provides a direct equivalence proof for minimax solutions of A.I. Subbotin and generalized weak solutions in the sense of idempotent analysis. It is shown that the Hamilton-Jacobi equation Vt+H(t, x,DxV ) = 0 (with the Hamiltonian H(t, x, s) concave in s), considered in the context of minimax generalized solutions, is linear w.r.t. ⊕ = min and ̄ = +. This leads to a representation fo...

A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module E over a Riemannian manifold M . Recently, this formula has been generalized to arbitrary Dirac operators [2]. In this paper we prove a supersymmetric version of the generalized Lichnerowicz formula, motivat...