Functional Analysis

1. Front Matter

   Pages I-XII

   PDF

2. Preliminaries

   • Kôsaku Yosida

   Pages 1-22

3. Semi-norms

   • Kôsaku Yosida

   Pages 23-68

4. Applications of the Baire-Hausdorff Theorem

   • Kôsaku Yosida

   Pages 68-81

5. The Orthogonal Projection and F. Riesz’ Representation Theorem

   • Kôsaku Yosida

   Pages 81-101

6. The Hahn-Banach Theorems

   • Kôsaku Yosida

   Pages 102-119

7. Strong Convergence and Weak Convergence

   • Kôsaku Yosida

   Pages 119-145

8. Fourier Transform and Differential Equations

   • Kôsaku Yosida

   Pages 145-193

9. Dual Operators

   • Kôsaku Yosida

   Pages 193-208

10. Resolvent and Spectrum

    • Kôsaku Yosida

    Pages 209-231

11. Analytical Theory of Semi-groups

    • Kôsaku Yosida

    Pages 231-274

12. Compact Operators

    • Kôsaku Yosida

    Pages 274-293

13. Normed Rings and Spectral Representation

    • Kôsaku Yosida

    Pages 294-362

14. Other Representation Theorems in Linear Spaces

    • Kôsaku Yosida

    Pages 362-378

15. Ergodic Theory and Diffusion Theory

    • Kôsaku Yosida

    Pages 379-418

16. The Integration of the Equation of Evolution

    • Kôsaku Yosida

    Pages 418-465

17. Back Matter

    Pages 467-498

    PDF

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 Uni­ 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 Springer­ 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 cor­ 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 BIER­ STEDT.

• Hilbert space
• Laplace operator
• Self-adjoint operator
• convolution
• differential equation
• differential operator
• distribution
• extrema
• functional analysis
• generalized function
• integral
• integration
• maximum
• operational calculus
• operator

• Gakushuin University, Tokyo, Japan

  Kôsaku Yosida

Policies and ethics