The Regularized Trace for Nuclear Perturbations of Discrete Operators
The spectra of general differential operators in the direct sum spaces
In this paper, the general ordinary quasi-differential expression of -th order with complex coefficients and its formal adjoint on any finite number of intervals , , are considered in the setting of the direct sums of -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...
The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...
The stability radius of a bundle of closed linear operators
Time Dependent Perturbations and Scattering of Strongly Continuous Groups on Banach Spaces.
Time-dependent Scattering Theory.
Time-dependent Schrödinger perturbations of transition densities
We construct the fundamental solution of for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We...
Trace Formula for Nonnuclear Perturbations of Selfađoint Operators
Trace formula for nuclear perturbations of discrete nonselfadjoint operators.
Trace Formulas of Gelfand--levitan Type
Über das Wachstum von Resolventen in der Nähe einer isolierten Singularität.
Über die Approximation von linearen Glechungen zweiter Art und Eigenwertproblemen in Banach-Räumen.
Über die Stabilität von Eigenwerten.
Über Kommutatoren und Störungsmetriken und ihre Beziehung zum Funktionalkalkül.
Unitary equivalence of operators and dilations
Given two contractions T and T' such that T'-T is an operator of finite rank, we prove, under some conditions, the unitary equivalence of the unitary parts of the minimal isometric dilations (respectively minimal co-isometric extensions) of T and T'.
Weyl spectra and Weyl's theorem
"Weyl's theorem" for an operator on a Hilbert space is the statement that the complement in the spectrum of the Weyl spectrum coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl's theorem survives for polynomials of operators and under quasinilpotent or compact perturbations. First, we show that if T is reduced by each of its finite-dimensional eigenspaces then the Weyl spectrum obeys the spectral mapping theorem, and further if T is reduction-isoloid...
Weyl type theorems for p-hyponormal and M-hyponormal operators
"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for every f ∈...
Weyl's theorems and Kato spectrum.
Weyl's type theorems and perturbations.
Zur asymptotischen Störungstheorie für Eigenwertaufgaben mit diskreten Teilspektren.