相关论文: Spectrum of a linear differential equation with co…
We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the…
In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded ``core'', with finitely many unbounded tubes attached to it. We adopt an elementary and purely variational point of view,…
In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
Let $X$ and $G$ be compact Lie groups, $F_1:X\to X$ the time-one map of a $C^\infty$ measure-preserving flow, $\phi:X\to G$ a continuous function and $\pi$ a finite-dimensional irreducible unitary representation of $G$. Then, we prove that…
We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for…
Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations $a(xb)=c$ and $a(bx)=c$ over the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We give a complete characterization of the spectrum of composition operators, induced by an automorphism of the open unit disk, acting on a family of Banach spaces of analytic functions that includes the Bloch space and BMOA. We show that…
We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are…