Related papers: Perturbations of embedded eigenvalues for the plan…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
We provide eigenvalue asymptotics for a Dirac-type operator on $\mathbb Z^n$, $n\geq 2$, perturbed by multiplication operators that decay as $|\mu|^{-\gamma}$ with $\gamma<n$. We show that the eigenvalues accumulate near the value of the…
Persistent Laplacians are matrix operators that track how the shape and structure of data transform across scales and are popularly adopted in biology, physics, and machine learning. Their eigenvalues are concise descriptors of geometric…
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…
We discuss quantum graphs consisting of a compact part and semiinfinite leads. Such a system may have embedded eigenvalues if some edge lengths in the compact part are rationally related. If such a relation is perturbed these eigenvalues…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps in a metric space are…
I revisit the so called "bispectral problem" introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues,…
We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an…
This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the…
In this work, we investigate the discrete spectrum generated by complex matrix-valued perturbations for a class of 2D and 3D Pauli operators with nonconstant magnetic fields. We establish a simple criterion for the potentials to produce…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
We show that spectral Hausdorff dimensional properties of discrete Schr\"oodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations,…
We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex $\ell^p$-potentials for $1\leq p\leq\infty$. As a corollary, subsets of the essential spectrum free of embedded…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We initiate the study of cortex algebras (commutative Banach algebras with extendable multiplicative-linear functionals) and the spectral permanence property. In addition, we analyze some particular examples in this context and present open…
This paper is devoted to the study of preservation of eigenvalues, Jordan structure and complementary invariant subspaces of structured matrices under structured perturbations. Perturbations and structure-preserving perturbations are…
In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lam\'e operators with non self-adjoint perturbations, we provide…