THE THEORY OF FRACTIONAL POWERS OF OPERATORS

This is a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research since the publication in 1987 of the paper by G. Dore and A. Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained.