In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology.
Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980s. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory of Lagrangian...
In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of ...
This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups).
The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the...
This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appea...
This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots, Jones and HOMFLYPT polynomials.
Knot theory has expanded enormously since the first edition of this book published in 1985. In this third completely...
This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred...
Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin...
Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riem...
Themonograph contains a study on various function classes, a number of new results and new or easy proofs of old result (Fefferman Stein theorem on subharmonic behavior, theorem on conjugate functions on Bergman spaces), which might be interesting for specialists, a full discussion on g-function (all p > 0), and a treatment of lacunary series with values in quasi-Banach spaces.
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Themonograph contains a study on various function classes, a number of new results and new or easy proofs of old result (Fefferman Stein theorem on...
Geometric group theory studies groups as realized as symmetries of metric spaces. One of the most important classes of groups are `hyperbolic groups', the subject of this book. They have a beautiful and robust theory, which is explored from the beginning of the theory right up to the forefront of current research. It will suitable for an advanced graduate class, or for study by those beginning in the field provide a reference for experts and outsiders alike. The book starts from the beginning (at a level appropriate for graduate students just beginning in the field) and works up to somewhere...
Geometric group theory studies groups as realized as symmetries of metric spaces. One of the most important classes of groups are `hyperbolic groups',...
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves, and Gelfand pairs refer to pairs of groups satisfying certain properties on restricted representations. This book contains written material of lectures on the topic which might serve as an introduction to the topic.
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves, and Gelfan...
This ambitious and substantial monograph, written by prominent experts in the field, presents the state of the art of convexity, with an emphasis on the interplay between convex analysis and potential theory; more particularly, between Choquet theory and the Dirichlet problem. The book is unique and self-contained, and it covers a wide range of applications which will appeal to many readers.
This ambitious and substantial monograph, written by prominent experts in the field, presents the state of the art of convexity, with an emphasis o...
This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided.
This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connecti...
This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory based on symmetric Markov processes and developed further in conjunction with the stochastic analysis based on additive functional.
Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the...
This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is...
