Related papers: The essential spectrum of advective equations
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
Contrary to prevailing notion we find that the spectrum associated with the extended states in a complex system may belong to the Poisson universality class if the system is subjected to a specific set of constraints. Our results are based…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact…
The local spectrum of a vertex set in a graph has been proven to be very useful to study some of its metric properties. It also has applications in the area of pseudo-distance-regularity around a set and can be used to obtain quasi-spectral…
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…
The essential spectrum of multiparticle Brown-Ravenhall operators is characterized in terms of two--cluster decompositions for a wide class of external fields and interparticle interactions and for the systems with prescribed symmetries.
This is to review some recent progress in PDE. The emphasis is on (energy) supercritical nonlinear Schr\"odinger equations. The methods are applicable to other nonlinear equations.
We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential spectrum has been known to be difficult, given that…
The scope of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE). For monoparametric families of PDE/DDE's, that are known to possess isolated…
We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak g}$-valued connections, for a simply-laced Lie algebra $\mathfrak g$. We prove that subdominant solutions to the ODE defined in different fundamental representations…
In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{\"o}dinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two…
We analyze the spectrum of the generalized Schrodinger operator in $L^2(R^\nu) \nu \geq 2$, with a general local, rotationally invariant singular interaction supported by an infinite family of concentric, equidistantly spaced spheres. It is…
Spiral waves emerge in numerous pattern forming systems and are commonly modeled with reaction-diffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…