In this paper, the changes of representations of a group are used in order to describe its action as algebraic Galois group of an univariate polynomial on the roots of factors of any Lagrange resolvent. By this way, the Galois group of resolvent factors are pre-determinated. In follows, different applications are exposed; in particular, some classical results of algebraic Galois theory.

We prove that the author’s powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the polynomial are differentially independent over constants. By definition, the terms of a resolvent lie in...

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrödinger ...

Using methods analogous to those introduced in Doney (2005), we express the resolvent density of a (killed) reflected Lévy process in terms of the resolvent density of the (killed) Lévy process. As an application we find a previously unknown identity for the potential density for killed reflected symmetric stable processes.

Finite-rank expansions of the two-body resolvent operator are explored as a tool for calculating the full three-dimensional two-body T -matrix without invoking the partial-wave decomposition. The separable expansions of the full resolvent that follow from finite-rank approximations of the free resolvent are employed in the Low equation to calculate the T-matrix elements. The finite-rank expansi...

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.

Abstract