Bøger i Grundlehren der mathematischen Wissenschaften serien

Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL.

The aim of this book is to serve as a reference text to provide an orientation in the enormous material which probability theory has accumulated so far. ed., New York 1960 (Chapter I, 1 of Chapter V) may serve as a first introduction to the various problems of probability theory.

The modem theory of Markov processes has its origins in the studies of A. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform.

In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;;

The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems.

Ever since my days as a student, economists, doctors, physiologists, biologists, and engineers have come to me with queries of a statistical nature. Study of the literature and my own ideas have repeat edly led me to improved methods, which will be established here and applied to instructive examples taken from the natural and social sciences.

The aim of this book is to give a systematic study of questions con cerning existence, uniqueness and regularity of solutions of linear partial differential equations and boundary problems. Functional analysis and distribution theory form the framework for the theory developed here.

An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.

The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. Contents 1 Introduction . . . . . . . Transcendental Theory . Hasse Invariants . The a --+ a' Map .

First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on groups and designs, and Blake-Mullin [1] on coding theory, whereas no compre hensive book exists on (a) and (b).

The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. Selberg's fonnula . Wirsing's inequality .