Bøger i Springer Monographs in Mathematics serien

Covering a wide range of material, this volume describes fundamental aspects of representation theory of the Virasoro algebra. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and more.

This book covers the properties and structure of positive linear maps of operator algebras into the bounded operators on Hilbert space.

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises.

It covers classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups, giving unified treatment of several different problems.

This book explores the fundamentals of total domination in graphs, the interplay with transversals in hypergraphs and the association with diameter-2-critical graphs. Includes several proofs, and a toolbox of proof techniques for attacking open problems.

This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

This book considers problems of optimization arising in the design of electromagnetic radiators and receivers, presenting a systematic general theory applicable to a wide class of structures. References to mathematics and engineering literature guide readers through the necessary mathematical background.

This is the revised and enlarged 2nd edition of the authors' original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory.

This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

The purpose of this text is to provide a self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, this one begins with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion.

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

This book offers a clear and comprehensible introduction to incidence geometry, including such topics as projective and affine geometry and the theory of buildings and polar spaces. More than 200 figures make even complicated proofs accessible to the reader.

This comprehensive, encyclopedic text provides the reader - from the graduate student to the researcher/practitioner - with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research.

This introduction to modern set theory opens the way to advanced current research. Coverage includes the axiom of choice and Ramsey theory, and a detailed explanation of the sophisticated technique of forcing. Offers notes, related results and references.

As well as explaining the use of ultrasound in the process, this volume proposes a new, 'solitary wave' method of evaluating complex, microstructured materials such as alloys and composites. It includes numerical examples and analysis of the solutions.

This book surveys 20th century progress in classical number theory, from the proof of the Prime Number Theorem in 1896 through the proof of Fermat's Last Theorem, focusing on the part of number theory that addresses properties of integers and rational numbers.

This book shows how to calculate arbitrarily high orders of derivatives of the Douglas Energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations.

Presenting current results on analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes, this book covers distribution of points on the sphere, the reconstruction algorithm in computerized tomography and more.

With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov's first method, tackling ordinary differential equations expressed as series form.

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems.

This book covers dimension theory, ANR theory (theory of retracts) and related topics, connecting with various fields in geometric and general topology. Many proofs are illustrated by figures or diagrams, making it easier to understand the underlying concepts.

This book offers a comprehensive overview of dimension theory of hyperbolic flows. It includes a detailed discussion of major open problems in the area.

This monograph provides a self-contained introduction to non-commutative multiple-valued logic algebras. It includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, and pseudo-MV algebras.

Based on the author's lectures at Cornell Probability Summer School in 2012, this book links the concept of superconcentration with probability theory. Includes a number of open problems for professional mathematicians and exercises for graduate students.

Mathematical Methods for Elastic Plates

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties.

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals.

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years.

This book describes classic and new results on solvability and unsolvability of equations in explicit form, presenting the author's complete exposition of topological Galois theory, plus basics of the Picard-Vessiot theory and a great deal more.