Calculus and mathematical analysis Books

Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods,...

The authors explore a unifying model which couples phase separation and damage processes in a system of partial differential equations. The model has technological applications to solder materials where interactions of both phenomena have been observed...

This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Köhne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physically...

The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter­ points mining and investigating a...

"Signal Processing and Systems Theory" is concerned with the study of H-optimization for digital signal processing and discrete-time control systems. The first three chapters present the basic theory and standard ...

Testprozesse I,ll, ••• , XI zur Simulation: siehe Isermann (1987), Bd.I Je nach ZweckmaBigkeit wird als Dimension fur die Zeit in Sekunden "s" oder "sec" verwendet ("sec" urn Verwechslungen mit der Laplace­ Variablen s = 6 + i...

Kommutative Algebren, in denen als Ersatz des Assoziativgesetzes 2 2 die Identitat (u v) u = u (v u) gilt, wurden erstmals von P. JORDAN im Jahre 1932 im Zusammenhang mit Fragen der Quantentheorie untersucht. Die Autoren P...

Dieses Buch will weder ein Lehrbuch der Funktionalanalysis noch eines der numerischen Mathematik sein; sondern es mochte nur zeigen, wie sich in der numerischen Mathematik in neuerer Zeit ein 5truktur­ wandel vollzogen hat, wie...

This book is an elementary introduction to non-classical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a...

My original introduction to this subject was through conservations, and ultimate­ ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various...

Investigations in modem nonlinear analysis rely on ideas, methods and prob­ lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex­...

This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and...

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce...

Geometrical (in particular, topological) methods in nonlinear analysis were originally invented by Banach, Birkhoff, Kellogg, Schauder, Leray, and others in existence proofs. Since about the fifties, these methods turned out to...

In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most...

Since the appearance, in 1970, of Vol. I of the present monograph 1370], the theory of bases in Banach spaces has developed substantially. Therefore, the present volume contains only Ch. III of the monograph, instead of Ch...

Stone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical...

The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the ...

The investigation of the relationships between compact Riemann surfaces (al­ gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A...

This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier...

Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between...

The fundamental problem of the theory of Fourier series consists of the investigation of the connections between the metric properties of the function expanded, the behavior of its Fourier coefficients {cn} with respect to an...

Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as...

The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A...

The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are...

15 Liapunov's "second method" eliminates this drawback and leads to accurate conclusions regarding the stability of well-defined families of systems. This method made it natural to introduce the new notion of "absolute...

Integration in function spaces arose in probability theory when a gen­ eral theory of random processes was constructed. Here credit is cer­ tainly due to N. Wiener, who constructed a measure in function space, integrals-with...

This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical...

A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard...

This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students'...

Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to...

There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of...

For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation...

1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1 < f < v, where Pis a linear...

When I first considered writing a book about multipliers, it was my intention to produce a moderate sized monograph which covered the theory as a whole and which would be accessible and readable to anyone with a basic knowledge...

The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation...

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of...

Homogeneous cosmological models, self-similar motion of self-gravitating gas and motion of gas with homogeneous deformation have important applica­ tions in the theory of evolution of the universe. In particular they can be...

In preparing the English edition of this unique work, every effort has been made to obtain an easily read and lueid exposition of the material. This has frequently been done at the expense of a literal translation of the...

It is the author's aim to give a systematic account of the most im­ portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved...

This work grew out of Errett Bishop's fundamental treatise 'Founda­ tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author...

Infinite series, and their analogues-integral representations, became funda­ mental tools in mathematical analysis, starting in the second half of the seven­ teenth century. They have provided the means for introducing into...

General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a...

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate...