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

We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in…

Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different…

We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of…

We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.

We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…

For operators defined on locally convex spaces we define the notions of boundedness and ergodicity associated to an infinite matrix. Given two matrices $ A$ and $ B$, we study when $ A$-bounded operators are $ B$-ergodic. Using this…

We establish exponential decay in H\"older norm of transfer operators applied to smooth observables of uniformly and nonuniformly expanding semiflows with exponential decay of correlations.

We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…

The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the…

The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.

The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.

We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the…

We derive explicit inequalities for sums of eigenvalues of one-dimensional Schr\"{o}dinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit…

Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…

In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the…

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.

We construct an expansion in generalized eigenfunctions for Schrodinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.

Lower bounds for the first and the second eigenvalue of uniform hypergraphs which are regular and linear are obtained. One of these bounds is a generalization of the Alon-Boppana Theorem to hypergraphs.

In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.