Bücher der Reihe Lehrbucher und Monographien aus dem Gebiete der exakten Wissenschaften

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfangen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen fur die historische wie auch die disziplingeschichtliche Forschung zur Verfugung, die jeweils im historischen Kontext betrachtet werden mussen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfangen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen fur die historische wie auch die disziplingeschichtliche Forschung zur Verfugung, die jeweils im historischen Kontext betrachtet werden mussen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Covers some of the salient features of classical, one variable complex function theory. This book develops and exploits methods of all three of the principal schools (those of Cauchy, Riemann and Weierstrass).

At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans­ forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu­ tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.

Die Behandlung der Leguminosen in der Chemotaxonomie der Pflanzen wird mit Band XIb-1 fortgesetzt. In ihm werden die von den Caesalpinioideae und Mimosoideae bekannt gewordenen Naturstoffe im Rahmen der natürlichen Klassifikation der Familie besprochen. Der Teilband enthält über 2000 Literaturhinweise sowie ein eigenes Pflanzennamen- und Stichwortregister. Hegnauer's Chemotaxonomie is an indispensable handbook for all those scientific disciplines concerned with not only systematic botany, but all aspects of the plant world. Both text and bibliography reflect our present knowledge of the particularities of plant metabolism. The last volume of Chemotaxonomy of Plants treats Leguminosae in three parts. XIa.: General aspects. XIB-1: Phytochemistry and chemotaxonomy of Caesalpinioideae and Mimosoideae. XIb-2: Phytochemistry and chemotaxonomy of Papilionoideae (in preparation). These three volumes form a valuable tool for everyone with an interest in the Leguminosae. They are not only relevant to plant taxonomists, plant physiologists, and natural product chemists but also to ecologists, agriculturists, nutritional scientists, pharmacists, pharmacologists and ethnobotanists. The cosmopolitan Leguminosae cover approximately 600 genera and 13000 species including many economically and ethnobotanically important plants. Each of the three volumes devoted to Leguminosae contains a taxonomic index, a subject index and over 2000 references.

to Classical Complex Analysis Vol. 1 by Robert B. Burckel Kansas State University 1979 BIRKHAUSER VERLAG BASEL UND STUTTGART CIP-Kurztitelaufnahme der Deutschen Bibliothek Burckel, Robert B.: An introduction to classical complex analysis I by Robert B. Burckel. - Basel. Stuttgart: Birkhiiuser. Vol. I. - 1979. (Lehrbilcher und Monographien aus dem Gebiete der exakten Wissenschaften: Math. Reihe; Bd. 64) All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner. © Birkhiiuser Verlag Basel, 1979 North and South America Edition published by ACADEMIC PRESS. INC. III Fifth Avenue, New York, New York 10003 (Pure and Applied Mathematics, A Series of Monographs and Textbooks, Volume 82) ISBN-13: 978-3-0348-9376-3 e-ISBN-13: 978-3-0348-9374-9 DOl: 10.1007/978-3-0348-9374-9 Library of Congress Catalog Card Number 78-67403 5 Contents Volume I PREFACE 9 Chapter 0 PREREQUISITES AND PRELIMINARIES 13 § 1 Set Theory 13 § 2 Algebra 14 § 3 The Battlefield 14 § 4 Metric Spaces 15 § 5 Limsup and All That 18 § 6 Continuous Functions 20 § 7 Calculus 21 Chapter I CURVES, CONNECTEDNESS AND CONVEXITY 22 § 1 Elementary Results on Connectedness 22 § 2 Connectedness of Intervals, Curves and Convex Sets 23 § 3 The Basic Connectedness Lemma 28 § 4 Components and Compact Exhaustions 29 § 5 Connectivity of a Set 33 § 6 Extension Theorems 37 Notes to Chapter I 39

The theory of the Lebesgue integral is still considered as a difficult theory, no matter whether it is based the concept of measure or introduced by other methods. divides the leather into a finite number of vertical strips and considers the strips approximately as rectangles.