Spectral concentration in Sturm-Liouville equations with large negative potential.
Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions.
Sturm-Liouville operator with general boundary conditions.
Sur le spectre de quelques opérateurs et les variétés de Jacobi
The basis property in of the boundary value problem rationally dependent on the eigenparameter
We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in ...
The dependence of the eigenvalues of the Sturm-liouville problem on boundary conditions
The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula
The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an -dimensional matrix eigenvalue problem is derived with a special matrix , that is, if is odd.Based on the product formula, an integration method with a fictitious time, namely...
The formulation of second-order boundary value problems on time scales.
The ratio of eigenvalues of the Dirichlet eigenvalue problem for equations with one-dimensional -Laplacian.
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...
Upper bounds for the eigenvalues of differential equations.
Variational inclusions for a Sturm-Liouville type differential inclusion
We establish several variational inclusions for solutions of a nonconvex Sturm-Liouville type differential inclusion on a separable Banach space.
Various half-eigenvalues of scalar -Laplacian with indefinite integrable weights.
Wiener amalgam spaces for the fundamental identity of Gabor analysis.
In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general time-frequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen duality principle and the Janssen representation of a Gabor frame operator. All these results are closely connected with the so-called Fundamental Identity of Gabor Analysis, which we derive from an application of Poisson's summation formula for the symplectic...
Zeros of the Jost function for a class of exponentially decaying potentials.
Асимптотика по спектральному параметру решений Вийля уравнений Штурма-Лиувилля
Индефинитные эллиптические спектральные задачи
Многоточечные аппроксимации Паде в обратной задаче Штурма-Лиувилля
О дискретности спектра нелинейного уравнения Штурма - Лиувилля четвертого порядка
О спектральной матрице уравнения Штурма-Лиувилля с ограниченным на оси примесным потенциалом.