Series: Operator Theory: Advances and Applications, Vol. 248
2016, Approx. 605 p.
A product of Birkhauser Basel
Printed book
Hardcover
ISBN 978-3-319-21014-8
Presents the first comprehensive account of the two-weight theory
of basic integral operators, developed in variable exponent Lebesgue
spaces
Provides the complete characterizations of Riesz potentials (of
functions in variable Lebesgue spaces), weights and space exponents
Explores the weak and strong type estimates criteria for fractional
and singular integrals
Introduces new function spaces that unify variable exponent
Lebesgue spaces and grand Lebesgue spaces
This book, the result of the authorsf long and fruitful collaboration, focuses on integral
operators in new, non-standard function spaces and presents a systematic study of the
boundedness and compactness properties of basic, harmonic analysis integral operators
in the following function spaces, among others: variable exponent Lebesgue and
amalgam spaces, variable Holder spaces, variable exponent Campanato, Morrey and Herz
spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue
spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized
grand Morrey spaces, and weighted analogues of some of them.
The results obtained are widely applied to non-linear PDEs, singular integrals and PDO
theory. One of the bookfs most distinctive features is that the majority of the statements
proved here are in the form of criteria.
The book is intended for a broad audience, ranging from researchers in the area to experts
in applied mathematics and prospective students.
Series: Progress in Mathematics, Vol. 311
2016, Approx. 150 p.
A product of Birkhauser Basel
Printed book
Hardcover
ISBN 978-3-319-21304-0
Explores common structures in different fields of homological
algebra: homology of classical groups, rational cohomology of
algebraic groups, and algebraic topology
Serves as an introduction to homological algebra
Highlights recent applications in a concise and accessible format
This book features a series of lectures, that explores three different fields in which functor
homology (short for homological algebra in functor categories) has recently played
a significant role. For each of these applications, the functor viewpoint provides both
essential insights and new methods for tackling difficult mathematical problems.
In the lectures by Aurelien Djament, polynomial functors appear as coefficients in the
homology of infinite families of classical groups, e.g. general linear groups or symplectic
groups, and their stabilization. Djamentfs theorem states that this stable homology can be
computed using only the homology with trivial coefficients and the manageable functor
homology. The series includes an intriguing development of Scorichenkofs unpublished
results.
The lectures by Wilberd van der Kallen lead to the solution of the general cohomological
finite generation problem, extending Hilbertfs fourteenth problem and its solution to
the context of cohomology. The focus here is on the cohomology of algebraic groups, or
rational cohomology, and the coefficients are Friedlander and Suslinfs strict polynomial
functors, a conceptual form of modules over the Schur algebra.
Roman Mikhailovfs lectures highlight topological invariants: homotopy and homology of
topological spaces, through derived functors of polynomial functors. In this regard the
functor framework makes better use of naturality, allowing it to reach calculations that
remain beyond the grasp of classical algebraic topology.
Lastly, Antoine Touzefs introductory course on homological algebra makes the book
accessible to graduate students new to the field.
The links between functor homology and the three fields mentioned above offer
compelling arguments for pushing the development of the functor viewpoint. By
gathering these lectures, the editors hope to give the reader a feel for functors, and a
valuable new perspective to apply to their favourite problems.
Series: Advanced Courses in Mathematics - CRM Barcelona
2016, Approx. 240 p.
A product of Birkhauser Basel
Printed book
Softcover
ISBN 978-3-0348-0932-0
Provides applications to the study of periodic solutions for some well
know differential equations and Hamiltonian systems
Includes new ideas and techniques for central configurations in
spaces with dimension bigger than three
Presents invariant objects in dynamical systems in a unique
combination of analytical and geometrical aspects
The notes of this book originate from three series of lectures given at the Centre de
Recerca Matematica (CRM) in Barcelona. The first one is dedicated to the study of periodic
solutions of autonomous differential systems in Rn via the Averaging Theory and was
delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on
methods for studying Central Configurations. The last one, by Carles Simo, describes the
main mechanisms leading to a fairly global description of the dynamics in conservative
systems.
The book is directed towards graduate students and researchers interested in dynamical
systems, in particular in the conservative case, and aims at facilitating the understanding
of dynamics of specific models. The results presented and the tools introduced in this
book include a large range of applications.
Series: Applied Mathematical Sciences, Vol. 152
2016, Approx. 560 p.
Printed book
Hardcover
ISBN 978-3-662-47506-5
Contains a lot of theorems, with full proofs, a true piece of
mathematical Analysis
Offers a detailed, rigorous, and self-contained presentation of the
theory of hyperbolic conservation laws from the basic theory to the
forefront of research
Treats the scalar case as well as the case of systems of conservation
laws
Displays a lot of details and information about numerical
approximation for the Cauchy Problem
Suitable for graduate courses in PDEs and numerical analysis
This is the second edition of a well-received book providing the fundamentals of the
theory hyperbolic conservation laws. Several chapters have been rewritten, new material
has been added, in particular, a chapter on space dependent flux functions, and the
detailed solution of the Riemann problem for the Euler equations.
Hyperbolic conservation laws are central in the theory of nonlinear partial differential
equations and in science and technology. The reader is given a self-contained
presentation using front tracking, which is also a numerical method. The multidimensional
scalar case and the case of systems on the line are treated in detail. A chapter on finite
differences is included.
From the reviews of the first edition:
"It is already one of the few best digests on this topic. The present book is an excellent
compromise between theory and practice. Students will appreciate the lively and accurate
style." D. Serre, MathSciNet
"I have read the book with great pleasure, and I can recommend it to experts as well
as students. It can also be used for reliable and very exciting basis for a one-semester
graduate course." S. Noelle, Book review, German Math. Soc.
"Making it an ideal first book for the theory of nonlinear partial differential equations...an
excellent reference for a graduate course on nonlinear conservation laws." M. Laforest,
Comp. Phys. Comm.
Series: Lecture Notes in Mathematics, Vol. 2150
2016, Approx. 275 p.
Printed book
Softcover
ISBN 978-3-319-22703-0
This is an introduction to the mathematics behind the phrase gquantum Lie algebrah.
The numerous attempts over the last 15-20 years to define a quantum Lie algebra as
an elegant algebraic object with a binary gquantumh Lie bracket have not been widely
accepted. In this book, an alternative approach is developed that includes multivariable
operations. Among the problems discussed are the following: a PBW-type theorem;
quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie
operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--
Umirbaev operations for the Lie theory of nonassociative products. Opening with an
introduction for beginners and continuing as a textbook for graduate students in physics
and mathematics, the book can also be used as a reference by more advanced readers.
With the exception of the introductory chapter, the content of this monograph has not
previously appeared in book form.
Advanced Series on Statistical Science & Applied Probability: Volume 21
344pp Jun 2015
ISBN: 978-981-4678-58-2 (hardcover)
Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.
Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.
The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.
In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.
Random Change of Time
Integral Representations and Change of Time in Stochastic Integrals
Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis
Stochastic Exponential and Stochastic Logarithm. Cumulant Processes
Processes with Independent Increments. Levy Processes
Change of Measure. General Facts
Change of Measure in Models Based on Levy Processes
Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes
Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case
Martingale Measures in the Stochastic Theory of Arbitrage
Change of Measure in Option Pricing
Conditionally Brownian and Levy Processes. Stochastic Volatility Models
A Wider View. Ambit Processes and Fields, and Volatility/Intermittency
Readership: Mathematical researchers, graduate students and practitioners interested in application of probabilistic theories & stochastic processes to economics & finance, and to turbulence.