Generators and Interpolation
Herbert Amann · Birkhäuser Basel eBooks · 1995
The abstract theory of linear parabolic problems, developed in the first part of this treatise, rests on two cornerstones: on the theory of analytic semigroups and on interpolation theory. In the first section of this chapter we discuss in some detail the classes of generators of analytic semigroups that are used throughout. In the second section we review the fundamentals of interpolation theory. We also introduce the class of ‘admissible interpolation functors’ that, on the one hand, is flexible enough to build an easy and general abstract theory of evolution equations on it, and, on the other hand, is general enough to cover all applications occurring in practice. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.