On the eigenfunctions of the complex Ornstein-Uhlenbeck operators

Abstract

Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators in the complex Hilbert space $L_{\Cnum}^2(μ)$. We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.

16pages

References in corpus (1)

• L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

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