相关论文: Evans Functions, Jost Functions, and Fredholm Dete…
We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line. The applications we have in mind include linear stability…
Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the $2$-modified characteristic…
The Evans function is a well known tool for locating spectra of differential operators in one spatial dimension. In this paper we construct a multidimensional analogue as the modified Fredholm determinant of a ratio of Dirichlet-to-Robin…
For a second order difference equation that arises in the study of stability of unidirectional (generalized Kolmogorov) flows for the Euler equations of ideal fluids on the two dimensional torus, we relate the following five functions of…
We study the point spectrum of a second order difference operator with complex potential on the half-line via Fredholm determinants of the corresponding Birman-Schwinger operator pencils, the Evans and the Jost functions. An application is…
We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green's functions associated with closed ordinary differential…
The concept of parity due to Fitzpatrick, Pejsachowicz and Rabier is a central tool in the abstract bifurcation theory of nonlinear Fredholm operators. In this paper, we relate the parity to the Evans function, which is widely used in the…
By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill's method for numerical approximation of spectra of…
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary…
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine…
We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a representation of the $n$th minor as an…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
The diagonal spin-spin correlations of the square lattice Ising model, originally expressed as Toeplitz determinants, are given by two distinct Fredholm determinants - one with an integral operator having an Appell function kernel and…
We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schr\"odinger operator on a half-line to a simple Wronski determinant of…
The Evans function is a tool for assessing the stability of travelling wave solutions for partial differential equations. A recent paper (math.NA/0605581) analyzes the order reduction experienced when evaluating the Evans function…
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been…
We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral representation in terms of the symbol of the original…
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum of boundary value problems arising in the…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…