Related papers: Explicit a priori bounds on transfer operator eige…

We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…

For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…

Estimates for the total multiplicity of eigenvalues for Schr\"odinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.

The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

For first order systems, we obtain an efficient bound on the exponential decay of an eigenfunction in terms of the distance between the corresponding eigenvalue and the essential spectrum. As an example, the Dirac operator is considered.

Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions…

For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find…

We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural…

Following Escobar [Esc97] and Jammes [Jam15], we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary…

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…

We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.

We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of…

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum of a bounded operator on a bi complex Hilbert space is…

Using the Fourier transform, we obtain upper bounds for sums of eigenvalues of the free plate.

Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is…

We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…