Year: 1966
Type: article
Abstract: A definition of fractional (or complex) powers A°>, a e C, is given for closed linear operators A in a Banach space X with the resolvent set containing the negative real ray (-oo, 0) and such that {λ(λ + A)" 1 ; 0 < λ < oo} is bounded; fundamental properties such as additivity (A*A β = A a+ P), coincidence with the iterations A* = A n for integers a = n, and analytic dependence on a are discussed.Since the fractional powers A* are generally unbounded in both of the cases Re a > 0 and Re a < 0, attention is paid to the domains D{A ω ), which are related to the spaces D σ and R τ of xeX defined by the regularity of (Λ + A)" 1 ^ at oo and 0. When -A generates a bounded continuous semi-group or a bounded analytic semi-group, more detailed results are obtained.
Source: Pacific Journal of Mathematics
Author: Hikosaburo Komatsu
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W655862175