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Develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and...Savoir plus
Contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. The author devotes most of ...Savoir plus
Focuses on the fundamentals of a theory, which is an analog of affine algebraic geometry for partial differential equations. This work describes appli...Savoir plus
Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. I...Savoir plus
Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mat...Savoir plus
Presents an introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. This book also include ...Savoir plus
Presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole p...Savoir plus
Intends to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of...Savoir plus
Covers topics including fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and ...Savoir plus
Presents the analysis of optimal control problems for systems described by partial differential equations. This book covers cases where the controlled...Savoir plus
Hilbert $C^*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C}$ is replaced by an arbitrary $C...Savoir plus
Focuses on the sequential methods of solving a class of problems to which belongs, for example, the problem of finding a maximum point of a function i...Savoir plus
Based on lectures on geometric function theory given by the author at Leningrad State University, this book studies univalent conformal mapping of sim...Savoir plus
This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by W...Savoir plus
The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a ...Savoir plus
Offers a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. Introducing fundam...Savoir plus
Divided in two parts, this book presents an introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order ellip...Savoir plus
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean cur...Savoir plus
Presents examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transfo...Savoir plus
In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations...Savoir plus
Provides a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies ...Savoir plus
Lie groups are very general mathematical objects that appear in numerous areas such as topology, functional analysis, and algebra, as well as differen...Savoir plus
An introduction to the work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its modifications and generalizations, including a m...Savoir plus
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation $F(\...Savoir plus