Hasil untuk "math.SP"

Ilia Binder, David Damanik, Michael Goldstein et al.

We characterize spectra of Schrödinger operators with small quasiperiodic analytic potentials in terms of their comb domains, and study action variables motivated by the KdV integrable system.

Petr Zemánek

The spectrum of an arbitrary self-adjoint extension of the minimal linear relation associated with the discrete symplectic system in the limit point case is completely characterized by using the limiting Weyl--Titchmarsh $M_+(λ)$-function. Furthermore, a dependence of the spectrum on a boundary condition is investigated and, consequently, several results of the singular Sturmian theory are derived.

Benjamin Delarue, Guendalina Palmirotta

We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Schröder.

David Borthwick, Yiran Wang

We prove existence results and lower bounds for the resonances of Schrödinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions and asymptotics of the scattering phase.

Natalia P. Bondarenko

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases

Alexander Makin

Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the root function system forms a usual Riesz basis rather than a Riesz basis with parentheses.

Martin Karuhanga

In this paper, quantitative upper estimates for the number of eigenvalues lying below the essential spectrum of Schroedinger operators with potentials generated by Ahlfors regular measures in a strip subject to two different types of boundary conditions (Robin and Dirichlet respectively) are presented. The estimates are presented in terms of weighted L^1 norms and Orlicz norms of the potential.

Yonca Sezer, Özlem Bakşi

In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.

Kang Lv

We consider the inverse Sturm-Liouville problem with one discontinuous point on three-star graph, we deduced the distribution of the eigenvalues, and proved that one spectrum could uniquely determine the unknown potential and jump information when we know the whole potentials on two edges and half potential on another edge.

Peter Yuditskii

We derive Fourier integral associated to the complex Martin function in the Denjoy domain of Widom type with the Direct Cauchy Theorem (DCT). As an application we study reflectionless Weyl-Titchmarsh functions in such domains, related to them canonical systems and transfer matrices. The DCT property appears to be crucial in many aspects of the underlying theory.

Jialun Li

Let M be a geometrically finite rank one locally symmetric manifolds. We prove that the spectrum of the Laplace operator on M is finite in a small interval which is optimal.

Sinan Ariturk

On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant vertices. For trees, these estimates are sharp. We also establish sharp upper bounds for the spectral gap of the complete graph $K_4$. The proofs are based on estimates for eigenvalues on graphs with Dirichlet conditions imposed at the pendant vertices.

Philippe Briet, Mounira Gharsalli

In this paper we study the influence of an electric field on a two dimen-sional waveguide. We show that bound states that occur under a geometrical deformation of the guide turn into resonances when we apply an electric field of small intensity having a nonzero component on the longitudinal direction of the system. MSC-2010 number: 35B34,35P25, 81Q10, 82D77.

Yiwei Dong

It is shown that there exist systems having almost specification property and zero entropy. Since Sigmund has shown that systems with specification property must have positive entropy, this result reveals further the difference between almost specification and specification. Moreover, one can step on to obtain a both sufficient and necessary condition to ensure positive entropy.

Natalia Bondarenko

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the necessary and sufficient conditions on the Weyl matrix of the non-self-adjoint matrix Sturm-Liouville operator. We also investigate the self-adjoint case and obtain the characterization of the spectral data as a corollary of our general result.

Hikmet Kemaloglu

In this study, inverse nodal problem is solved for p-Laplacian Schrödinger equation with energy-dependent potential with the Drichlet conditions. Asymptotic estimates of eigenvalues, nodal points and nodal lengths are given by using Prüfer substitution. Especially, an explicit formula for potential function is given by using nodal lengths. Results are more general than classical p- Laplacian Sturm Liouville problem. For the proofs, it is used the methods given in the references <cite>lav3</cite>, <cite>Wang</cite>.

Anne Boutet de Monvel, Daniel Lenz, Peter Stollmann

We prove a variant of Sch'nol's theorem in a general setting: for generators of strongly local Dirichlet forms perturbed by measures. As an application, we discuss quantum graphs with $δ$- or Kirchhoff boundary conditions.

Alexander Kiselev

We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and periodic Schrödinger operators is preserved under perturbations by all potentials $V(x)$ satisfying $|V(x)| \leq C(1+x)^{-\frac{2}{3}-ε}.$ The main new technique includes an a.e.\ convergence theorem for a class of integral operators.

Azamat M. Akhtyamov

An uniqueness theorem for the inverse problem in the case of a second-order equation defined on the interval [0,1] when the boundary forms contain combinations of the values of functions at the points 0 and 1 is proved. The auxiliary eigenvalue problems in our theorem are chose in the same manner as in Borg's uniqueness theorem are not as in that of Sadovni\v ci$\check \imath $'s. So number of conditions in our theorem is less than that in Sadovni\v ci$\check\imath$'s.

A. A. Abramov, A. Aslanyan, E. B. Davies

We obtain bounds on the complex eigenvalues of non-self-adjoint Schrödinger operators with complex potentials, and also on the complex resonances of self-adjoint Schrödinger operators. Our bounds are compared with numerical results, and are seen to provide useful information.