The D Bar Neumann Problem And Schrödinger Operators

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The d-bar Neumann Problem and Schrödinger Operators

Friedrich Haslinger
The d bar Neumann Problem and Schr dinger Operators Book PDF

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 348 pages
File Size : 52,7 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9783110377835

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The d-bar Neumann Problem and Schrödinger Operators by Friedrich Haslinger Pdf

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

Friedrich Haslinger
The d bar Neumann Problem and Schr dinger Operators Book PDF

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 252 pages
File Size : 42,7 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9783110315356

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The d-bar Neumann Problem and Schrödinger Operators by Friedrich Haslinger Pdf

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 ond-bar spaces over bounded pseudoconvex domains and on weightedd-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

Emil J. Straube
Lectures on the L2 Sobolev Theory of the d bar Neumann Problem Book PDF

Author : Emil J. Straube
Publisher : European Mathematical Society
Page : 220 pages
File Size : 52,6 Mb
Release : 2010
Category : Mathematics
ISBN : 3037190760

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Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem by Emil J. Straube Pdf

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

Walter Roth
Integral Representation Book PDF

Author : Walter Roth
Publisher : Walter de Gruyter GmbH & Co KG
Page : 266 pages
File Size : 42,5 Mb
Release : 2023-10-04
Category : Mathematics
ISBN : 9783111315478

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Integral Representation by Walter Roth Pdf

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.

Complex Algebraic Foliations

Alcides Lins Neto,Bruno Scárdua
Complex Algebraic Foliations Book PDF

Author : Alcides Lins Neto,Bruno Scárdua
Publisher : Walter de Gruyter GmbH & Co KG
Page : 249 pages
File Size : 41,8 Mb
Release : 2020-02-24
Category : Mathematics
ISBN : 9783110602050

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Complex Algebraic Foliations by Alcides Lins Neto,Bruno Scárdua Pdf

This book is a basic reference in the modern theory of holomorphic foliations, presenting the interplay between various aspects of the theory and utilizing methods from algebraic and complex geometry along with techniques from complex dynamics and several complex variables. The result is a solid introduction to the theory of foliations, covering basic concepts through modern results on the structure of foliations on complex projective spaces.

Groups of Prime Power Order

Yakov G. Berkovich,Zvonimir Janko
Groups of Prime Power Order Book PDF

Author : Yakov G. Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 475 pages
File Size : 51,7 Mb
Release : 2015-12-14
Category : Mathematics
ISBN : 9783110381559

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Groups of Prime Power Order by Yakov G. Berkovich,Zvonimir Janko Pdf

This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa’s theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra.

The Elementary Theory of Groups

Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman
The Elementary Theory of Groups Book PDF

Author : Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman
Publisher : Walter de Gruyter GmbH & Co KG
Page : 321 pages
File Size : 45,9 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110342031

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The Elementary Theory of Groups by Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman Pdf

After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.

Complex Analysis

Friedrich Haslinger
Complex Analysis Book PDF

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 347 pages
File Size : 46,7 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9783110426151

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Complex Analysis by Friedrich Haslinger Pdf

In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators

Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order. Volume 5

Yakov G. Berkovich,Zvonimir Janko
Yakov Berkovich Zvonimir Janko Groups of Prime Power Order Volume 5 Book PDF

Author : Yakov G. Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 433 pages
File Size : 42,5 Mb
Release : 2016-01-15
Category : Mathematics
ISBN : 9783110295351

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Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order. Volume 5 by Yakov G. Berkovich,Zvonimir Janko Pdf

This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.

Applied Nonlinear Functional Analysis

Nikolaos S. Papageorgiou,Patrick Winkert
Applied Nonlinear Functional Analysis Book PDF

Author : Nikolaos S. Papageorgiou,Patrick Winkert
Publisher : Walter de Gruyter GmbH & Co KG
Page : 622 pages
File Size : 47,9 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9783110532982

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Applied Nonlinear Functional Analysis by Nikolaos S. Papageorgiou,Patrick Winkert Pdf

The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.

Yakov G. Berkovich; Lev S. Kazarin; Emmanuel M. Zhmud': Characters of Finite Groups. Volume 2

Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud'
Yakov G Berkovich Lev S Kazarin Emmanuel M Zhmud Characters of Finite Groups Volume 2 Book PDF

Author : Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud'
Publisher : Walter de Gruyter GmbH & Co KG
Page : 725 pages
File Size : 53,6 Mb
Release : 2018-12-17
Category : Mathematics
ISBN : 9783110224092

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Yakov G. Berkovich; Lev S. Kazarin; Emmanuel M. Zhmud': Characters of Finite Groups. Volume 2 by Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud' Pdf

This updated edition of this classic book is devoted to ordinary representation theory and is addressed to finite group theorists intending to study and apply character theory. It contains many exercises and examples, and the list of problems contains a number of open questions.

Classifying the Absolute Toral Rank Two Case

Helmut Strade
Classifying the Absolute Toral Rank Two Case Book PDF

Author : Helmut Strade
Publisher : Walter de Gruyter GmbH & Co KG
Page : 394 pages
File Size : 55,5 Mb
Release : 2017-04-10
Category : Mathematics
ISBN : 9783110517606

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Classifying the Absolute Toral Rank Two Case by Helmut Strade Pdf

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case

Volume 1

Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud'
Volume 1 Book PDF

Author : Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud'
Publisher : Walter de Gruyter GmbH & Co KG
Page : 623 pages
File Size : 50,8 Mb
Release : 2017-12-18
Category : Mathematics
ISBN : 9783110224078

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Volume 1 by Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud' Pdf

This updated edition of this classic book is devoted to ordinary representation theory and is addressed to finite group theorists intending to study and apply character theory. It contains many exercises and examples, and the list of problems contains a number of open questions.

Structure Theory

Helmut Strade
Structure Theory Book PDF

Author : Helmut Strade
Publisher : Walter de Gruyter GmbH & Co KG
Page : 550 pages
File Size : 47,8 Mb
Release : 2017-04-24
Category : Mathematics
ISBN : 9783110515442

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Structure Theory by Helmut Strade Pdf

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras

Global Affine Differential Geometry of Hypersurfaces

An-Min Li,Udo Simon,Guosong Zhao,Zejun Hu
Global Affine Differential Geometry of Hypersurfaces Book PDF

Author : An-Min Li,Udo Simon,Guosong Zhao,Zejun Hu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 54,8 Mb
Release : 2015-08-17
Category : Mathematics
ISBN : 9783110268898

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Global Affine Differential Geometry of Hypersurfaces by An-Min Li,Udo Simon,Guosong Zhao,Zejun Hu Pdf

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.