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Functional Analysis with Current Applications in Science, Technology and Industry
This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996. Topics include topological vector spaces, Banach algebras, meromorphic functions, partial differential equations, variational equations and inequalities, optimization, wavelets, elastroplasticity, numerical integration, fractal image compression, reservoir simulation, forest management, and industrial maths.
Topology and Maps
This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for...
Metrizable Barrelled Spaces
This text draws together a number of recent results concerning barrelled locally convex spaces, from general facts involving cardinality and dimensionality to barrelledness of some familiar vector-valued or scalar-valued normed spaces of functional analysis, and providing a study of some of these spaces. Throughout the exposition, the authors show the strong relationship between barrelledness properties and vector-valued measure theory.
Integral Expansions Related to Mehler-Fock Type Transforms
An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.
Integral Representations For Spatial Models of Mathematical Physics
This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems. The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics. This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.
Conjugate Gradient Type Methods for Ill-Posed Problems
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublish...
A Survey of Preconditioned Iterative Methods
The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
A Generalized Taylor's Formula for Functions of Several Variables and Certain of its Applications
The classical Taylor's formula of advanced calculus is generalized, extending the notion of the differentiability class Cm, with applications to maxima and minima and to sufficiency of jets.
Recent Advances in Differential Equations
The First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997. Researchers from around the world attended-including representatives from the US, Canada, and the Netherlands-but the majority of the speakers hailed from China and Hong Kong. This volume contains the plenary lectures and invited talks presented at that conference, and provides an excellent view of the research on differential equations being carried out in China. Most of the subjects addressed arose from actual applications and cover ordinary and partial differential equations. Topics include:
