Related papers: Spectrality of ordinary differential operators
In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace…
Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for…
The theory of second order complex coefficient operators of the form $\mathcal{L}=\mbox{div} A(x)\nabla$ has recently been developed under the assumption of $p$-ellipticity. In particular, if the matrix $A$ is $p$-elliptic, the solutions…
We consider a spectral stability estimate by Burenkov and Lamberti concerning the variation of the eigenvalues of second order uniformly elliptic operators on variable open sets in the N-dimensional euclidean space, and we prove that it is…
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…
In this paper, we consider a class of matrix functions, which contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of order $n \ge 2$. We show that every matrix function of this…
Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator $T$, $$\widetilde{\sigma}_i(f(T)) = f(\widetilde{\sigma}_i(T)), $$ for several extended essential spectra…
We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of…
The differential operators pencil recovery uniqueness theorem is proved in our article. Novelty of this result is not equation coefficient recovery, but boundary conditions coefficients recovery. We show that all conditions of the theorem…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
In this contribution we investigate the Schr\"ordinger equation associated to the Laplacian on the sphere in the form of sharp Strichartz estimates. We will provided simple proofs for our main theorems using purely the $L^2\rightarrow L^p$…
We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for Laplace-Beltrami and Schr\"odinger operators. Our results…
The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and…
We obtain precise asymptotics for the Steklov eigenvalues on a compact Riemannian surface with boundary. It is shown that the number of connected components of the boundary, as well as their lengths, are invariants of the Steklov spectrum.…
We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…
In this paper we revisit an approach pioneered by Auchmuty to approximate solutions of the Laplace- Robin boundary value problem. We demonstrate the efficacy of this approach on a large class of non-tensorial domains, in contrast with other…
The concept of near resonances for harmonic approximations of semiclassical Schr\"odinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the…
In the smooth scattering theory framework, we consider a pair of self-adjoint operators $H_0$, $H$ and discuss the spectral projections of these operators corresponding to the interval $(-\infty,\lambda)$. The purpose of the paper is to…