Eigenvalue approximation
Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics
For a class of non-selfadjoint –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...
Ein Äquikonvergenzsatz für eine Klasse von singulären Differentialoperatoren.
Ein Homomorphiesatz und verwandte Operatoren in topologischen Vektorräumen.
Ein „merkwürdiges” Spektrum für nichtlineare Operatoren
We define a spectrum for Lipschitz continuous nonlinear operators in Banach spaces by means of a certain kind of "pseudo-adjoint" and study some of its properties.
Ein neues Surjektivitätskriterium im Hilbertraum.
Ein Pólyasches Momentenproblem und umhüllende asymptotische Potenzreihen.
Ein Störungssatz für abgeschlossene, lineare Operatoren.
Ein Zerlegungssatz für Resolventen elliptischer Operatoren.
Eine Bemerkung zur Division von Distributionen durch analytische Operatorfunktionen.
Eine Bemerkung zur Lösung der Operatorgleichung
Eine Existenzausgabe für asymptotisch lineare Störungen eines Fredholmoperators mit Index 0.
Eine Funktionalgleichung für operatorwertige Funktionen.
Einschliessungsaussagen für Differentialoperatoren vierter Ordnung und ein Verfahren zur Berechnung von Schrankenfunktionen.
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...
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.
Embedding theorems for Müntz spaces
We discuss boundedness and compactness properties of the embedding , where is the closed linear span of the monomials in and is a finite positive Borel measure on the interval . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from ...
Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....
Enclosures and semi-analytic discretization of boundary value problems
Endpoint estimates from restricted rearrangement inequalities.