Equations of the first kind and the inversion of series of resolvents of a closed operator

Banach空间上算子笔的本原方程的基本方程

The fundamental equations for inversion of operator pencils on Banach space

本文研究Banach空间上算子笔的本原方程，证明解析性与Laurent级数系数满足的基本方程的关系，并探讨其在谱分离性质中的应用。

Inversion of operator pencils on Banach space using Jordan chains when the generalized resolvent has an isolated essential singularity

We assume that the generalized resolvent for a bounded linear operator pencil mapping one Banach space onto another has an isolated essential singularity at the origin and is analytic on some annular region of the complex plane centred at the origin. In such cases the resolvent operator can be represented on the annulus by a convergent Laurent series and the spectral set has two components---a bounded component inside the inner boundary of the annulus and an unbounded component outside the outer boundary. In this paper we prove that the complementary spectral separation projections on the doma…

Inverses of generators of integrated fractional resolvent operator functions

This paper is devoted to the inverse generator problem in the setting of generators of integrated resolvent operator functions. It is shown that if the operator $A$ is the generator of a tempered $β$-times integrated $α$-resolvent operator function ($(α,β)$-ROF) and it is injective, then the inverse operator $A^{-1}$ is the generator of a tempered $(α,γ)$-ROF for all $γ> β+1/2,$ by means of an explicit representation of the integrated resolvent operator function based in Bessel functions of first kind. Analytic resolvent operator functions are also considered, showing that $A^{-1}$ is in addit…

Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides

We present an inversion formula which can be used to obtain resolvent expansions near embedded thresholds. As an application, we prove for a class of quantum waveguides the absence of accumulation of eigenvalues and the continuity of the scattering matrix at all thresholds.

论 $H+A^{*}+A$ 的预解式

On the resolvent of $H+A^{*}+A$

本文给出类 QFT 哈密顿量 $H+A^*+A$ 自伴实现结果的更简证明，显式表示其预解式与定义域，并通过 Krein 型公式将其刻画为带重整化抵消项的截断哈密顿量的范数预解极限。

Surjection and inversion for locally Lipschitz maps between Banach spaces

We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdifferential, as well as the notion of pseudo-Jacobians in the infinite-dimensional setting, which are the analog of the pseudo-Jacobian matrices defined by Jeyakumar and Luc. Using these notions, we derive our results about existence and uniqueness of solution for nonlinear equations. In particular, …