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Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint $h$ –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Ein neues Surjektivitätskriterium im Hilbertraum.

Hermann Sohr (1981)

Monatshefte für Mathematik

Équations d'évolution en norme uniforme (conditions nécessaires et suffisantes de résolution et holomorphie)

G. Lumer (1976/1977)

Séminaire Équations aux dérivées partielles (Polytechnique)

Ergodic theorems and perturbations of contraction semigroups

Marta Tyran-Kamińska (2009)

Studia Mathematica

We provide sufficient conditions for sums of two unbounded operators on a Banach space to be (pre-)generators of contraction semigroups. Necessary conditions and applications to positive emigroups on Banach lattices are also presented.

Expansions and eigenfrequencies for damped wave equations

Michael Hitrik (2001)

Journées équations aux dérivées partielles

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds,...

Extensions, dilations and functional models of infinite Jacobi matrix

B. P. Allahverdiev (2005)

Czechoslovak Mathematical Journal

A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation....