Related papers: Accumulation of Complex Eigenvalues of a Class of …
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We study a problem of Jeong and Taniguchi asking to find all rational maps which are Ahlfors functions. We prove that the rational Ahlfors functions of degree two are characterized by having positive residues at their poles. We then show…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
This paper is concerned with {an extension and reinterpretation} of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. {We state} two general abstract results on…
We study the phenomenon of an eigenvalue emerging from essential spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential. We prove the sufficient conditions for the existence and absence of such…
We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting the system dynamics using a one-hot representation of the system state, we derive a matrix representation of the Koopman operator as a transpose of the…
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
We prove the exponential decay of eigenfunctions of reductions of Brown-Ravenhall operators to arbitrary irreducible representations of rotation-reflection and permutation symmetry groups under the assumption that the corresponding…
We prove a HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential…
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…
Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy-Hilbert space of analytic functions with inner product defined by integration over a period on the boundary of the strip. Simple examples show…
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…
In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…
We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…