Scales of banach spaces, theory of interpolation and their applications (Uniwersytet Śląski)

Tytuł Scales of Banach Spaces, Theory of Interpolation and their Applications Autor Łukasz Dawidowski Język angielski Wydawnictwo Uniwersytet Śląski ISBN 978-83-8012-525-4 kolekcja Prace Naukowe UŚ; Matematyka Rok wydania 2012 Katowice Wydanie 1 ilość stron 110 Format pdf Spis treści Contents Preface / 7 Chapter 1 Fractional powers of operators / 11 Chapter 2 Interpolation spaces / 17 2.1. Spaces Dσp / 18 2.2. Definition of interpolation spaces S(p; θ;X; p; θ – 1; Y ) / 23 2.3. Complex interpolation space / 25 2.4. Another definition of interpolation spaces; Real interpolation space / 27 2.4.1. The K-method / 28 2.4.2. The trace method / 30 2.4.3. The Reiteration Theorem / 32 2.4.4. Some examples / 33 Chapter 3 Infinitesimal generators of semi-groups / 35 3.1. Infinitesimal generators of bounded semi-groups / 35 3.2. Infinitesimal generators of bounded analytic semi-groups / 36 Chapter 4 Scales of Banach Spaces / 39 4.1. Inductive Limits and Projective Limits of Sequences of Banach Spaces / 40 4.2. Regular Spaces and Hyper-spaces / 51 Chapter 5 Examples of scales of Banach spaces / 63 Chapter 6 Sectorial Operators / 71 6.1. Examples of Sectorial Operators / 73 Chapter 7 Applications / 79 Chapter 8 The abstract Cauchy problem / 89 8.1. Examples and applications / 90 Appendix A Theory of distributions and the Fourier transform / 99 A.1. Theory of distributions / 99 A.2. The Fourier transform of rapidly decreasing functions / 100 A.3. The Fourier transform of tempered distributions / 101 Bibliography / 103 Streszczenie / 107 Резюме / 107