Einschliessungsaussagen für Differentialoperatoren vierter Ordnung und ein Verfahren zur Berechnung von Schrankenfunktionen.
Ekeland's variational principle in locally p-convex spaces and related results
In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.
Elastoplastic reaction of a container to water freezing
The paper deals with a model for water freezing in a deformable elastoplastic container. The mathematical problem consists of a system of one parabolic equation for temperature, one integrodifferential equation with a hysteresis operator for local volume increment, and one differential inclusion for the water content. The problem is shown to admit a unique global uniformly bounded weak solution.
Electronic density at the nucleus. On a conjecture of Lieb
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
Elementary operators and subhomogeneous -algebras. II.
Elementary operators on Banach algebras and Fourier transform
We consider elementary operators , acting on a unital Banach algebra, where and are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of functions...
Elementary operators on prome C*-algebras. I.
Elementary Tauberian Theorems For Regular Linear Operators
Elementary Tauberian theorems for regular linear operators.
Elements of C*-algebras commuting with their Moore-Penrose inverse
We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.
Elliptic and degenerate-elliptic operators in unbounded domains
Elliptic Boundary Problems and the Boutet de Monvel Calculus in Besov and Triebel-Lizorkin Spaces.
Elliptic corner operators in spaces with continuous radial asymptotics II
Asymptotic expansions at the origin with respect to the radial variable are established for solutions to equations with smooth 2-dimensional singular Fuchsian type operators.
Elliptic Equations with Noninvertible Fredholm Linear Part and Bounded Nonlinearities.
Elliptic perturbations for Hammerstein equations with singular nonlinear term.
Elliptic regularity and essential self-adjointness of Dirichlet operators on
Elliptic resonance problems with unequal limits at infinity.
Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold
We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.