Related papers: The eigenvalues and eigenfunctions of the toroidal…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
Let $F$ be a totally real number field, $\mathcal{O}_{F}$ the ring of integers, $\mathfrak a$ and $\mathfrak I$ integral ideals and let $\chi$ a character of $\mathbb{A}_F^\times/F^\times$. For each prime ideal $\mathfrak{p}$ in…
We introduce two kinds of matrix-valued dynamical processes generated by nonnormal Toeplitz matrices with the additive rank 1 perturbations $\delta J$, where $\delta \in {\mathbb{C}}$ and $J$ is the all-ones matrix. For each process, first…
We consider the non-local operator ${\mathcal T}$ defined in 2-dimensional CFTs by the path integral over a torus with two punctures. Using the AdS/CFT correspondence, we study the spectrum and ground state of this operator in holographic…
The $n$-dimensional numerical range of a densely defined linear operator $T$ on a complex Hilbert space $\H$ is the set of vectors in $\C^n$ of the form $(< Te_1,e_1>,...,< Te_n,e_n>)$, where $e_1,...,e_n$ is an orthonormal system in $\H$,…
In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
The behaviour of the generalized Hilbert operator associated with a positive finite Borel measure $\mu$ on $[0,1)$ is investigated when it acts on weighted Banach spaces of holomorphic functions on the unit disc defined by sup-norms and on…
The finite Hilbert transform $T$ is a classical (singular) kernel operator which is continuous in every rearrangement invariant space $X$ over $(-1,1)$ having non-trivial Boyd indices. For $X=L^p$, $1<p<\infty$, this operator has been…
The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\lambda) = \exp(i(\lambda_1\psi_1 + ... + \lambda_n\psi_n)) for \lambda in R^n, gives rise to a manifold M of orthogonal projections…
We study the eigenvalues and eigenfunctions of the time-frequency localization operator $H_\Omega$ on a domain $\Omega$ of the time-frequency plane. The eigenfunctions are the appropriate prolate spheroidal functions for an arbitrary domain…
Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0…
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit…
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…
If $A(t)$ is a $C^{1,\al}$-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized $C^1$ in $t$. If $A$ is $C^\infty$ then the eigenvalues can be…
The definition of Toeplitz operators in the Bergman space $A^2(D)$ of square integrable analytic functions in the unit disk in the complex plane is extended in such way that it covers many cases where the traditional definition does not…