Functional Analysis
- PDF / 37,615,290 Bytes
- 469 Pages / 439.37 x 666.142 pts Page_size
- 99 Downloads / 296 Views
MATHEMATISCHEN WISSENSCHAFTEN IN EINZELDARSTELLUNGEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIETE HERAUSGEGEBEN VON
J. L. DOOB· E. HEINZ· F. HIRZEBRUCH E.HOPF· H.HOPF · W.MAAK · S. MAC LANE W . MAGNUS · F. K. SCHMIDT· K. STEIN GESCHAFrSFUHRENDE HERAUSGEBER
B. ECKMANN
UND
B.L.VAN DER WAERDEN ZURICH
BAND 123
Springer-Verlag Berlin Heidelberg GmbH 1966
FUNCTIONAL ANALYSIS BY
KOSAKU YOSIDA PROFESSOR OF MATHEMATICS AT THE UNIVERSITY OF TOKYO
2nd PRINTING CORRECTED
Springer-Verlag Berlin Heidelberg GmbH 1966
Geschaftsfiihrende Herausgeber :
Prof. Dr. B . Eckmann Eidgen ossische Technische Ho chschul e Ziirich
Prof. Dr. B . L. van der Waerden Mathe matisches Institut der Universitat Zurich
All rights reserved, espec ially that of translat ion into foreign language s. It is also forbidden to reproduce this book, either whole or in part, by photomech anical means (photostat, microfilm andj or m icrocard) o r an y other means with out written permission from the Publishers
© by Springer-Verlag Berlin Heidelberg 1965 Originally publi shed by Springer-Verlag Berlin Heidelberg New York in 1965. Library of Congress Catalog Card Number 64-8025
ISBN 978-3-662-23675-8 ISBN 978-3-662-25762-3 (eBook) DOI 10.1007/978-3-662-25762-3
T itel Nr . 5106
Preface The present book is based on lectures given by th e author at the Uni versit y of Tokyo during th e past ten ye ars. It is intended as a textbook to be studied by students on their own or t o be used in a course on Functional Analysis, i.e., th e general theory of linear operato rs in function spaces together with salient features of it s application to div erse fields of modern and classical analysis. Necessary prerequisit es for th e reading of this book are summarized, with or without proof, in Chapt er 0 under titles: Set Theory , Topological Spaces, Measure Spaces and Linear Sp aces. Then , sta rting with the chapter on Semi-n orms , a general theory of Ban ach and Hilbert spaces is pr esented in connection with t he theor y of generalized fun ctions of S. L. SOBOLEVand L. SCHWARTZ. Wh ile the book is primaril y addressed to gra dua te students , it is hoped it might prove useful to resear ch mathematicians , both pure and app lied. The reader may pass e.g. from Chapter IX (Analytical Theory of Semi-gro ups) dir ectly to Chapter XIII (Ergo dic Theory and Diffu sion Theory ) and to Chapter XIV (Integration of the E quation of Evolution). Such materi als as "Weak Topolo gies and Duality in Locally Convex Spaces" and " Nuclear Spaces" ar e presented in the form of the appendices t o Chapter V and Chap te r X, respectively. Th ese migh t be skipped for the first readin g by those who are inte reste d rather in th e application of lin ear opera tors. In th e pr eparation of the present book, the aut hor has received valu able advi ce and criticism from many friends. Especially, Mrs, K. HILLE has kindly read through the manuscript as well as the galley and page proofs. Without her painstaking help , this book could not have been printed in th e present st
