On the spectrum of non-selfadjoint differential operators.
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.
On weighted positivity of ordinary differential operators.
One-dimensional Schrödinger operators with local point interactions.
Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator.
Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen.
symmetric Schrödinger operators: reality of the perturbed eigenvalues.
Points tournants et résonances de Stark-Wannier
Property C for ODE and Applications to an Inverse Problem for a Heat Equation
Let , k = const > 0, j = 1,2, . Suppose that (*) for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0,1], which changes sign finitely many times, and solves the problem , 0 ≤ x ≤ 1, , . It is proved that (*) implies p = 0. This result is applied to an inverse problem for a heat equation.
Quantum-graph vertex couplings: some old and new approximations
In 1986 P. Šeba in the classic paper considered one-dimensional pseudo-Hamiltonians containing the first derivative of the Dirac delta function. Although the paper contained some inaccuracy, it was one of the starting points in approximating one-dimension self-adjoint couplings. In the present paper we develop the above results to the case of quantum systems with complex geometry.
Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step.
Remark to the problem of eigenvalues of Schrödinger equation
Renormalization of exponential sums and matrix cocycles
In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics
Résurgence de Voros et périodes des courbes hyperelliptiques
Le but de cet article est de formuler de façon géométrique l’idée maîtresse de Voros dans Ann. Inst. Henri Poincaré, Sect. A 39, 211-238 (1983) : les solutions de l’équation de Schrödinger stationnaire à une dimension, à potentiel polynomial, sont codées exactement dans le domaine complexe par leurs développements BKW (développements formels, divergents, en puissances de la constante de Planck), d’une façon entièrement lisible dans la géométrie des périodes de la forme (=variable de position,...
Self-adjoint boundary-value problems on time-scales.
Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
Semiclassical limit of the spectral decomposition of a Schrödinger operator in one dimension.
Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method
We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.
Some sharp inequalities for Dirac type operators.
Spectra of self-gradients on spheres.