Preface ......................................................... 5
Chapter 1. Linear operators ..................................... 9
1.1. Closable and closed operators ............................. 11
1.2. Symmetric and self-adjoint operators ...................... 17
Chapter 2. Semigroups of bounded operators ..................... 19
2.1. Strongly continuous semigroups ............................ 19
2.2. Analytic semigroups ....................................... 26
Chapter 3. Fractional powers of positive operators ............. 52
Chapter 4. Abstract parabolic equations ........................ 74
4.1. Homogeneous sectorial equations ........................... 74
4.2. Nonhomogeneous sectorial equations ........................ 75
4.3. Semilinear sectorial equations ............................ 82
Chapter 5. Examples and applications ........................... 92
5.1. Examples of sectorial operators ........................... 92
5.2. Applications to differential equations .................... 99
Appendix A. Compendium of useful information on the Bochner
integral .......................................... 105
Appendix B. Auxiliary results ................................. 112
Appendix С. Supplementary tools from the theory of PDEs ....... 113
References .................................................... 116
List of symbols ............................................... 118
Index ......................................................... 119
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