On the orthogonality of generalized eigenspaces for the Ornstein–Uhlenbeck operator
Journal article, 2021

We study the orthogonality of the generalized eigenspaces of an Ornstein–Uhlenbeck operator L in RN, with drift given by a real matrix B whose eigenvalues have negative real parts. If B has only one eigenvalue, we prove that any two distinct generalized eigenspaces of L are orthogonal with respect to the invariant Gaussian measure. Then we show by means of two examples that if B admits distinct eigenvalues, the generalized eigenspaces of L may or may not be orthogonal.

Ornstein–Uhlenbeck operator


Generalized eigenspaces

Gaussian measure


Valentina Casarino

University of Padua

Paolo Ciatti

University of Padua

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences

Archiv der Mathematik

0003-889X (ISSN) 1420-8938 (eISSN)

Vol. 117 5 547-556

Subject Categories

Algebra and Logic


Mathematical Analysis



More information

Latest update

4/5/2022 5