On the orthogonality of generalized eigenspaces for the Ornstein–Uhlenbeck operator
Artikel i vetenskaplig tidskrift, 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

Orthogonality

Generalized eigenspaces

Gaussian measure

Författare

Valentina Casarino

Università di Padova

Paolo Ciatti

Università di Padova

Peter Sjögren

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Archiv der Mathematik

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

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s00013-021-01637-6

Mer information

Senast uppdaterat

2021-08-17