Operator Methods in Shell Theory

Rotation methods in operator ergodic theory

Let E(·) : R → B(X) be the spectral decomposition of a trigonometrically well-bounded operator U acting on the arbitrary Banach space X, and suppose that the bounded function φ : T → C has the property that for each z ∈ T, the spectral integral R [0,2π] φ(e)dEz(t) exists, where Ez(·) denotes the spectral decomposition of the (necessarily) trigonometrically well-bounded operator (zU). We show th...

Methods of Kreĭn Space Operator Theory

The author was originally led to Krĕın space operator theory by a problem of L. de Branges concerning the coefficients of univalent functions. The particular question was resolved in the negative, but the operator methods used to show this are related to other areas which remain currently active, such as the study of generalized Schur and Nevanlinna functions. The methods are of a general natur...

Consistency of Iterative Operator-Splitting Methods: Theory and Applications

In this paper we describe a different operator-splitting method for decoupling complex equations with multi-dimensional and multiphysical processes for applications for porous media and phase-transitions. We introduce different operator-splitting methods with respect to their usability and applicability in computer codes. The error-analysis for the iterative operator-splitting methods is discus...

Operator Theory and Operator Algebras

Rotation operator formalism for open-shell omplexes