Related papers: Gordon type Theorem for measure perturbation

We prove a criterion for absence of eigenvalues for one-dimensional Schr\"odinger operators. This criterion can be regarded as an $L^1$-version of Gordon's theorem and it has a broader range of application. Absence of eigenvalues is then…

We study one-dimensional Schr\"odinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves a weak local periodicity condition. The criterion leads to sharp quantitative…

We review the recent developments in the spectral theory of discrete one-dimensional Schr\"odinger operators with potentials generated by substitutions and circle maps. We discuss how occurrences of local repetitive structures allow for…

We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition…

We give estimates for the changes of the eigenvalues of the Klein Gordon operator under the change of the potential. In some relevant situations we improve the existing estimates. We test our results on some exactly solvable models (Coulomb…

A Borg-type uniqueness theorem for matrix-valued Schr\"odinger operators is proved. More precisely, assuming a reflectionless potential matrix and spectrum a half-line $[0,\infty)$, we derive triviality of the potential matrix. Our approach…

Singular Gordon potentials are defined to be distributions from the space W^{-1}_{2,unif}(R) that are sufficiently fast approximated by periodic ones. We prove that Schr\"odinger operators with singular Gordon potentials have no point…

We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of frequency by the rationals, for a large class of…

Building on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schr\"odinger operators with almost reflective repetition potentials, we provide a new proof of the sharp Gordon's lemma, which…

Making use of the weighted Mourre theory developed in [GJ1], we show the limiting absorption principle for Schr{\"o}dinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of…

We consider a Schr\"odinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive…

We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schr\"odinger operators with a perturbed Wigner-Von Neumann potential at suitable energies. To our knowledge, this result is new…

A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values. We prove an analogue of Thompson's theorem for II_1…

We construct the one-dimensional analogous of von-Neumann Wigner potential to the relativistic Klein-Gordon operator, in which is defined taking asymptotic mathematical rules in order to obtain existence conditions of eigenvalues embedded…

We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation…

We consider the discrete versions of the well known Borg theorem and use simple linear algebraic techniques to obtain new versions of the discrete Borg type theorems. To be precise, we prove that the periodic potential of a discrete…

We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein-Gordon type Hamiltonian operators. We first study operators of the form $JG$, where $J$, $G$ are selfadjoint…

This paper presents the perturbation theory for the double--sine--Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation's influence. In particular case…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories is studied. We find a differential equation for the scalar potential, which incorporates all known cases where the 2 to n amplitudes at threshold vanish for all…