Paperback * ISBN 978-3-11-025030-5
Series: De Gruyter Textbook
to be published January 2012
Appropriate as a textbook for graduate courses or for independent study
Highly motivated by problems arising in various applications
Several exercises and summaries of each chapter help beginners to understand the material
This book provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their application to partial differential equations.
In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix.
The text is comprehensible for students of Mathematics and Physics with a basic education in Analysis.
Paperback | ISBN 978-3-11-025623-9
Series: De Gruyter Textbook
to be published January 2012
Now in paperback
With lots of exercises
Includes the new results and better proofs of the last 12 years
This is the second, edition of the successful book on the algebraic structure of the Stone-Cech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition.
This book is a self-contained exposition of the theory of compact right semigroups (sS, ・) for discrete semigroups (S, ・) and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.
Hardcover ISBN 978-3-11-025869-1
Series: De Gruyter Studies in Mathematics 43
to be published January 2012
Presents the basic ideas
Comes with a lot of practical applications
A topic on the borderline of Math, Physics, and Engeneering
Ideas from probability can be very useful to understand and motivate fractional calculus models for anomalous diffusion. Fractional derivatives in space are related to long particle jumps. Fractional time derivatives code particle sticking and trapping. This probabilistic point of view also leads to some interesting extensions, including vector fractional derivatives, and tempered fractional derivatives.
This book connects fractional diffusion equations, random walks, and statistical physics.
Hardcover | ISBN 978-3-11-025524-9
Series: Radon Series on Computational and Applied Mathematics 10
to be published May 2012
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the BV-norm have recently become very popular. Meanwhile the most well-known methods have been investigated for linear and nonlinear operator equations in Banach spaces. Motivated by these facts the authors aim at collecting and publishing these results in a monograph.
2012 | Hardcover | ISBN 978-3-11-025904-9
Series: Inverse and Ill-Posed Problems Series 56
to be published May 2012
Written by scientists for scientists
Applying the theoretical methods to scientific problems
Conveying statistical, regularization, and optimization methods
Inverse Problems and Applications in Science and Engineering represent an extremely active research field nowadays. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine and other areas of applications.
The intent of the book is to report recent advances of inversion theory and recent developments with practical applications in frontiers of sciences. Especially, the book reports inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography and astronomical imaging.
Each chapter is written by internationally active researchers in their research fields. This book can be served as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing and environmental science, will benefit from the contents of the book since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.
EMS Series of Lectures in Mathematics
ISBN 978-3-03719-096-8
DOI 10.4171/096
June 2011, 114 pages, softcover, 17 x 24 cm.
Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflo’s result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds.
All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley?Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details.
The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory.