Geodesic
Fundamental properties of fractional powers of unbounded operators in Banach spaces
Matematičeskie trudy, Tome 27 (2024) no. 3, pp. 20-29 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the classical theory of operator-valued analytic functions is extended to a wide class of linear unbounded operators, defined in Banach spaces on not everywhere dense sets. The properties of fractional powers of the corresponding operators are also established. The class under consideration includes Sturm–Liouville differential operators with homogeneous Dirichlet boundary conditions, acting in spaces of continuous functions on bounded intervals. 
@article{MT_2024_27_3_a1,
     author = {V. S. Belonosov and A. G. Shvets},
     title = {Fundamental properties of fractional powers of unbounded operators in {Banach} spaces},
     journal = {Matemati\v{c}eskie trudy},
     pages = {20--29},
     year = {2024},
     volume = {27},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2024_27_3_a1/}
}
TY  - JOUR
AU  - V. S. Belonosov
AU  - A. G. Shvets
TI  - Fundamental properties of fractional powers of unbounded operators in Banach spaces
JO  - Matematičeskie trudy
PY  - 2024
SP  - 20
EP  - 29
VL  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MT_2024_27_3_a1/
LA  - ru
ID  - MT_2024_27_3_a1
ER  - 
%0 Journal Article
%A V. S. Belonosov
%A A. G. Shvets
%T Fundamental properties of fractional powers of unbounded operators in Banach spaces
%J Matematičeskie trudy
%D 2024
%P 20-29
%V 27
%N 3
%U http://geodesic.mathdoc.fr/item/MT_2024_27_3_a1/
%G ru
%F MT_2024_27_3_a1
V. S. Belonosov; A. G. Shvets. Fundamental properties of fractional powers of unbounded operators in Banach spaces. Matematičeskie trudy, Tome 27 (2024) no. 3, pp. 20-29. http://geodesic.mathdoc.fr/item/MT_2024_27_3_a1/

[1] Fomin V. N., Mathematical Theory of Parametric Resonance in Linear Distributed Systems, Leningrad State University Press, L., 1972

[2] Yakubovich V. A., Starzhinskii V. M., Parametric Resonance in Linear Systems, Nauka, M., 1987

[3] Belonosov V. S., “Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations”, Sbornik: Mathematics, 208:8 (2017), 1088–1112 | DOI | DOI | MR

[4] Krylov N. M., Bogolyubov N. N., Introduction to Nonlinear Mechanics, Publishing House of the Academy of Sciences of the Ukrainian SSR, Kiev, 1937

[5] Mitropol'skii Yu. A., The Averaging Method in Nonlinear Mechanics, Naukova Dumka, Kiev, 1971

[6] Bogolyubov N. N., Mitropol'skii Yu. A., Asymptotic Methods in the Theo-ry of Nonlinear Oscillations, 4th edition, Nauka, M., 1974

[7] Krasnosel'skii M. A., Zabreiko P. P., Pustyl'nik E. I., Sobolevskii P. E., Integral Operators in Spaces of Summable Functions, Nauka, M., 1966

[8] Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–New York, 1966 | MR

[9] Krein S. G., Linear Differential Equations in Banach Spaces, Nauka, M., 1967