Related papers: The essential spectrum of advective equations
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
Spectral densities encode the relevant information characterising the system-environment interaction in an open-quantum system problem. Such information is key to determining the system's dynamics. In this work, we leverage the potential of…
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting…
There are classical theorems of analysis which, given certain conditions on a perturbation, assert stability of the essential and absolutely continuous components of the spectrum of a self-adjoint operator. Whereas the singular component is…
In this article, we consider a class of bi-stable reaction-diffusion equations in two components on the real line. We assume that the system is singularly perturbed, i.e. that the ratio of the diffusion coefficients is (asymptotically)…
We analyze all orthonormal bases of exponentials on the Cantor set defined by Jorgensen and Pedersen in J. Anal. Math. 75,1998, pp 185-228. A complete characterization for all maximal sets of orthogonal exponentials is obtained by…
We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.
We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles.…
The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…
Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…
We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions…
A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey--Stewartson II (DSII) equation. Discrete spectrum in the spectral problem corresponds to eigenvalues embedded into a…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
We investigate the spectrum of the two-dimensional Pauli operator, describing a spin-$1/2$ particle in a magnetic field $B$, with a negative scalar potential $V$ such that $|V|$ grows at infinity. In particular, we obtain criteria for…
We discuss three examples in which one may extend integrable Euler--Poincar\'e ODEs to integrable Euler--Poincar\'e PDEs in the matrix G-Strand context. After describing matrix G-Strand examples for $SO(3)$ and $SO(4)$ we turn our attention…
At the beginning of the study of the bispectral problem, see [18], the ad-conditions played a crucial role in finding non-classical instances. The connection with the ad-conditions has reappeared in several different incarnations of the…
The numerical range in the quaternionic setting is, in general, a non convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense,…
We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.