Operators Of Class C 0 With Spectra In Multiply Connected Regions
Download Operators Of Class C 0 With Spectra In Multiply Connected Regions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Operators Of Class C 0 With Spectra In Multiply Connected Regions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Operators of Class $C_0$ with Spectra in Multiply Connected Regions
In the present paper the author studies the analogue of the class [italic capital]C0 within a class of operators having a functional calculus based on the algebra of bounded holomorphic functions in a finitely connected domain with an analytic boundary. The latter class consists of the operators having the closure of the domain as a spectral set and having no normal direct summands with spectra contained in the boundary of the domain. (If the domain is the disk the preceding class reduces to the class of completely nonunitary contractions.) The basic properties known for the case of the disk, including the model theory, are established. The extension, even the mere construction of the functional calculus, is not routine, in part because it is unknown whether the analogue of Sz.-Nagy's dilation theorem is true in the author's multiply connected setting.
Harmonic Analysis of Operators on Hilbert Space
Author: Béla Sz Nagy
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-09-01
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Hodge Theory in the Sobolev Topology for the de Rham Complex
Author: Luigi Fontana
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.