Diagonalisation d’opérateurs non autoadjoints et séparation des variables. (Digonalisation of non self-adjoint operators and separation of variables). (French) Zbl 0559.47013

Geymonat, Giuseppe; Grisvard, Pierre

C. R. Acad. Sci., Paris, Sér. I 296, 809-812 (1983).

Let A be a closed linear operator in a Hilbert space H whose resolvent belongs to an appropriate Carleman class; the solutions of the equation \(\Psi ''(t)=A\Psi (t)\) are expandible in series of the generalized eigenvectors of A for large enough t. This allows separation of variables of the biharmonic equation in various domains.

MSC:

47A70	(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47E05	General theory of ordinary differential operators
47F05	General theory of partial differential operators

Keywords:

resolvent; Carleman class; expandible in series of the generalized eigenvectors; separation of variables of the biharmonic equation in various domains