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Fractional powers of operators
Open accessAbstract
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.
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Citations
Cited by
The Hamiltonian formalism and a many-valued analogue of Morse theory
Novikov, S. P. (1982) · Russian Mathematical Surveys · doi:10.1070/rm1982v037n05abeh004020 · Cited by 368
Representations of the fractional d’Alembertian and initial conditions in fractional dynamics
Calcagni, G., & Nardelli, G. (2025) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2025.117401 · Cited by 7
Metadata
- Authors
- Komatsu, H.
- Venue
- Pacific Journal of Mathematics
- Publisher
- Mathematical Sciences Publishers
- Published
- 1966-11-01
- Volume
- 19
- Issue
- 2
- Pages
- 285-346
- ISSN
- 0030-8730 (ISSN-L)
- OpenAlex
- W655862175
- Cited by
- 389
- References
- 0
- FWCI
- 10.43
- Type
- journal article
- Language
- en
- Open access
- bronze
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