Rochberg's abstract coboundary theorem revisited

Badea, Catalin; Devys, Oscar

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s11785-022-01293-w

Title :

Rochberg's abstract coboundary theorem revisited

Author(s) :

Badea, Catalin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Devys, Oscar [Auteur]

Journal title :

Complex Analysis and Operator Theory

Pages :

115

Publisher :

Springer Verlag

Publication date :

2022-09-29

ISSN :

1661-8254

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Rochberg's coboundary theorem provides conditions under which the equation (I-T)y = x is solvable in y. Here T is a unilateral shift on Hilbert space, I is the identity operator and x is a given vector. The conditions are ...
Show more >Rochberg's coboundary theorem provides conditions under which the equation (I-T)y = x is solvable in y. Here T is a unilateral shift on Hilbert space, I is the identity operator and x is a given vector. The conditions are expressed in terms of Wold-type decomposition determined by T and growth of iterates of T at x. We revisit Rochberg's theorem and prove a result for isometries. When T is merely a contraction,x is a coboundary under an additional assumption. Some applications to L2-solutions of the functional equation f(x) - f(2x) = F(x), considered by Fortet and Kac, are given.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Frontières de la théorie des opérateurs
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :