Flot hamiltonien et spectre d'un opérateur elliptique
Four characterizations of scalar-type operators with spectrum in a half-line
-scalar-type spectrality criterions for operators A whose resolvent set contains the negative reals are provided. The criterions are given in terms of growth conditions on the resolvent of A and the semigroup generated by A. These criterions characterize scalar-type operators on the Banach space X if and only if X has no subspace isomorphic to the space of complex null-sequences.
Fredholm, Riesz and local spectral theory of multipliers.
Functions of bounded variation on compact subsets of the plane
A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset σ of the plane. In this paper we define a new Banach algebra BV(σ) of functions of bounded variation on such a set and show that the function-theoretic properties of this algebra make it better suited to applications in spectral theory than those used previously....
Funktionalkalküle für abgeschlossene lineare Operatoren in Banachräumen.
Funktionalkalküle in mehreren Veränderlichen für stetige lineare Operatoren auf Banachräumen.