of the galley proof, correcting errors and improving the presentation. To all of them, the author expresses his warmest gratitude. Thanks are also due to Professor F. K. SCHMIDT of Heidelberg Uniยญ Yersity and to Professor T. KATO of the University of California at Berkeley who constantly encouraged the author to write up the present book. Finally, the author wishes to express his appreciation to Springerยญ Verlag for their most efficient handling of the publication of this book. Tokyo, September 1964 I{oSAKu YOSIDA Preface to the Second Edition In the preparation of this edition, the author is indebted to Mr. FLORET of Heidelberg who kindly did the task of enlarging the Index to make the book more useful. The errors in the second printing are corยญ rected thanks to the remarks of many friends. In order to make the book more up-to-date, Section 4 of Chapter XIV has been rewritten entirely for this new edition. Tokyo, September 1967 KOSAKU YOSIDA Preface to the Third Edition A new Section (9. Abstract Potential Operators and Semi-groups) pertaining to G. HUNT'S theory of potentials is inserted in Chapter XIII of this edition. The errors in the second edition are corrected thanks to kind remarks of many friends, especially of Mr. KLAUS-DIETER BIERยญ STEDT
CONTENT
0. Preliminaries -- I. Semi-norms -- II. Applications of the Baire-Hausdorff Theorem -- III. The Orthogonal Projection and F. Rieszโ Representation Theorem -- IV. The Hahn-Banach Theorems -- V. Strong Convergence and Weak Convergence -- VI. Fourier Transform and Differential Equations -- VII. Dual Operators -- VIII. Resolvent and Spectrum -- IX. Analytical Theory of Semi-groups -- X. Compact Operators -- XI. Normed Rings and Spectral Representation -- XII. Other Representation Theorems in Linear Spaces -- XIII. Ergodic Theory and Diffusion Theory -- XIV. The Integration of the Equation of Evolution
