The d-bar Neumann Problem and Schrödinger Operators
Title | The d-bar Neumann Problem and Schrödinger Operators PDF eBook |
Author | Friedrich Haslinger |
Publisher | Walter de Gruyter GmbH & Co KG |
Total Pages | 298 |
Release | 2014-08-20 |
Genre | Mathematics |
ISBN | 3110377837 |
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
The d-bar Neumann Problem and Schrödinger Operators
Title | The d-bar Neumann Problem and Schrödinger Operators PDF eBook |
Author | Friedrich Haslinger |
Publisher | Walter de Gruyter GmbH & Co KG |
Total Pages | 254 |
Release | 2014-08-20 |
Genre | Mathematics |
ISBN | 3110315351 |
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem
Title | Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem PDF eBook |
Author | Emil J. Straube |
Publisher | European Mathematical Society |
Total Pages | 220 |
Release | 2010 |
Genre | Mathematics |
ISBN | 9783037190760 |
This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.
Integral Representation
Title | Integral Representation PDF eBook |
Author | Walter Roth |
Publisher | Walter de Gruyter GmbH & Co KG |
Total Pages | 266 |
Release | 2023-10-04 |
Genre | Mathematics |
ISBN | 3111315479 |
This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.
Colloquium De Giorgi 2010-2012
Title | Colloquium De Giorgi 2010-2012 PDF eBook |
Author | Umberto Zannier |
Publisher | Springer Science & Business Media |
Total Pages | 80 |
Release | 2013-06-28 |
Genre | Mathematics |
ISBN | 8876424571 |
Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.
Abstracts of Papers Presented to the American Mathematical Society
Title | Abstracts of Papers Presented to the American Mathematical Society PDF eBook |
Author | American Mathematical Society |
Publisher | |
Total Pages | 826 |
Release | 2004 |
Genre | Mathematics |
ISBN |
Colloquium De Giorgi 2006
Title | Colloquium De Giorgi 2006 PDF eBook |
Author | Umberto Zannier |
Publisher | Springer |
Total Pages | 80 |
Release | 2007-05-10 |
Genre | Mathematics |
ISBN |
This book contains expositions of talks of the Colloquio De Giorgi, given by eminent experts and addressed to a ‘general’ public (audience) of mathematicians. The topics are prepared in such a way that readers will get some idea of recent progress in several mathematical fields.