Series: Operator Theory: Advances and Applications , Vol. 205
2010, Approx. 400 p., Hardcover
ISBN: 978-3-0346-0197-9
Due: February 2010
This volume is an outgrowth of the international workshop entitled "Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations" held at York University on August 4?8, 2009. It consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations. While the focus is on the current developments of pseudo-differential operators in the context of complex analysis and partial differential equations, other topics related to the analysis, applications and computations of pseudo-differential operators are featured.
Series: Progress in Mathematics , Vol. 283
2010, Approx. 305 p., Hardcover
ISBN: 978-3-0346-0208-2
Due: February 2010
This volume comprises the Lecture Notes of the CIMPA/TUBITAK Summer School Arrangements, Local systems and Singularities held at Galatasaray University, Istanbul during June 2007. The volume is intended for a large audience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related fields. The reader will find a variety of open problems involving arrangements, local systems and singularities proposed by the lecturers at the end of the school.
Preface and the List of Participants From the editors (written by Meral Tosun) Pencils of Plane Curves and Characteristic Varieties By Alexandru Dimca Combinatorics of Covers of Complexified Arrangements By Emanuele Delucchi Homological Aspects of Hyperplane Arrangements By Graham Denham Local Systems and Constructable Sheaves By Fouad El Zein, Jawad Snoussi Geometry and combinatorics of resonant weights By Michael Falk The characteristic quasi-polynomials of the arrangements and mid-hyperplane arrangements By Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao Toric varieties and the diagonal property By Ali Ulas Ozgur Kisisel, Ozer Ozturk Introduction To Plane Curve Singularity (Toric Resolution Tower And Puiseux Pairs) By Mutsuo Oka Surface Singularities Appeared In The Hyperbolic Schwarz Map For The Hypergeometric Equation By Takeshi Sasaki, Masaaki Yoshida On The Extendability of Free Multiarrangements By Masahiko Yoshinaga Lectures on Orlik-Solomon Algebras By Alexandru Dimca, Sergei Yuzvinsky Problem Session Edited by Ayse Altintas & Celal Cem Sarioglu
Series: Pseudo-Differential Operators , Vol. 3
2010, Approx. 350 p., Softcover
ISBN: 978-3-7643-8509-5
Due: March 2010
A thorough exposition of pseudodifferential calculus defined by metrics on the phase space
Contains a proof of the Nirenberg-Treves conjecture
Construction of counterexamples to "optimal" solvability under condition (psi)
This book contains three chapters. The first one, Basic Notions of Phase Space Analysis is only introductory. The second chapter, Metrics on the Phase Space, contains a thorough exposition of the Weyl calculus via a microlocalization procedure described by a metric on the phase space. The third chapter, Estimates for non-selfadjoint operators, is more involved and is devoted to a rather complete discussion of operators of principal type with complex-valued symbols.
Preface.- 1 Basic Notions of Phase Space Analysis.- 1.1 Introduction to pseudodifferential operators.- 1.2 Pseudodifferential operators on an open subset of Rn.- 1.3 Pseudodifferential operators in harmonic .- 2 Metrics on the Phase Space.- 2.1 The structure of the phase space.- 2.2 Admissible metrics.- 2.3 General principles of pseudodifferential calculus.- 2.4 The Wick calculus of pseudodifferential operators.- 2.5 Basic estimates for pseudodifferential operators.- 2.6 Sobolev spaces attached to a pseudodifferential calculus.- 3 Estimates for Non-selfadjoint Operators.- 3.1 Introduction.- 3.2 First bracket analysis.- 3.3 The geometry of condition (Y).- 3.4 The necessity of condition (Y).- 3.5 Estimates with loss of k/k + 1 derivative.- 3.6 Estimates with loss of one derivative.- 3.7 (Y) does not imply solvability with loss of one derivative.- 3.8 (Y) implies solvability with loss of 3/2 derivatives.- 3.9 Open problems.- 4 Appendix.- 4.1 Some elements of Fourier analysis.- 4.2 Some remarks of algebra.- 4.3 Lemmas of classical analysis.- 4.4 On the symplectic and metaplectic groups.- 4.5 Composing a large number of symbols.- 4.6 A few elements of operator theory.- 4.7 On Sjostrand algebra.- 4.8 On preparation theorems.- 4.9 On the pseudospectrum.- 4.10 More on symbolic calculus.
Series: Operator Theory: Advances and Applications , Vol. 201
2010, Approx. 385 p., Hardcover
ISBN: 978-3-0346-0210-5
Due: March 2010
This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in the area and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, and functional analysis. The material is of interest to experts, young researchers and postgraduate students.
Series: Operator Theory: Advances and Applications , Vol. 206
2010, Approx. 225 p., Hardcover
ISBN: 978-3-7643-8955-0
Due: March 2010
This volume contains English translations of 13 groundbreaking papers on Toeplitz matrices and Wiener-Hopf equations and other classes of discrete and continuous convolution operators and singular integral equations.
The papers are both of theoretical and numerical interest.
In particular, the papers examine fast algorithms for inversion of these operators, the theory of discrete and continuous resultants, inversion via factorization, and symbol construction. Originally the papers were written in Russian more than thirty years ago; their English translation is published here for the first time. These papers solved difficult problems and opened new venues in the above-mentioned areas. They are still frequently quoted, and moreover, they exert a continuing influence on numerical analysis and other areas of Pure and Applied Mathematics and Engineering.
The book is addressed to a wide audience of mathematicians and engineers, from graduate students to researchers, whose interests lie in the above-mentioned areas.
Part I Finite Toeplitz matrices and continuous analogs.- Inversion of finite Toeplitz matrices.- Inversion of finite Toeplitz matrices consisting of elements of a noncommutative algebra.- Matrix integral operators on a finite interval with kernels depending on the difference of the arguments.- The resultant matrix and its generalizations. I. The resultant operator for matrix polynomials.- The resultant matrix and its generalizations. II. The continual analogue of the resultant operator. Part II Singular integral operators. Algebras and Symbols.- The spectrum of singular integral operators in Lp spaces.- Algebra generated by the Toeplitz matrices in the spaces hp.- On singular integral equations with unbounded coefficients.- Singular integral equations with continuous coefficients on a composed contour.- On a local principle and algebras generated by Toeplitz matrices.- The symbol of singular integral operators on a composed contour.- One-dimensional singular integral operators with shift.- Algebras of singular integral operators with shift