Spectral analysis and synthesis
Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems.
Spectral analysis for differential operators with singularities.
Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
The paper is concerned with the spectral analysis for the class of linear operators in non-archimedean Hilbert space, where is a diagonal operator and is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). ...
Spectral analysis of a weighted shift operator with unbounded operator coefficients.
Spectral analysis of an operator associated with linear functional differential equations and its applications.
Spectral analysis of non-self-adjoint elliptic operators
Spectral analysis of relativistic atoms -- Dirac operators with singular potentials.
Spectral analysis of subordinate Brownian motions on the half-line
We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition...
Spectral Analysis of the Laplacian in Domains with Cylinders.
Spectral analysis of unbounded Jacobi operators with oscillating entries
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Spectral and homological properties of Hilbert modules over the disc algebra
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.
Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials
Spectral approach for kernel-based interpolation
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
Spectral approximation for Segal-Bargmann space Toeplitz operators
Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk or on the Segal-Bargmann space over . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression of A to the linear span of the monomials . Unfortunately, in general the spectrum of does not mimic the spectrum of A as...
Spectral approximation of multiplication operators.
Spectral approximation of positive operators by iteration subspace method
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators is also considered.
Spectral Asymmetrie and Zeta Functions.