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Mat. Zametki, 2015, Volume 97, Issue 2, Pages 174–190 (Mi mz10285)  

This article is cited in 18 scientific papers (total in 18 papers)

Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces

A. G. Baskakov

Voronezh State University

Abstract: Asymptotic representations of power bounded operators and bounded semigroups of linear operators acting in Banach spaces are obtained under the assumptions that the spectrum of bounded operators on the unit circle and the spectrum of the semigroup generator on the imaginary axis are countable. The methods of abstract harmonic analysis and the spectral theory of operators were used.

Keywords: power bounded operator, operator semigroup, harmonic analysis, spectral theory, asymptotic representation, Banach algebra.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00378
Russian Science Foundation 14-21-00066
This work was supported by the Russian Foundation for Basic Research (grant no. 13-01-00378) by the Russian Science Foundation (grant no. 14-21-00066 at Voronezh State University).


DOI: https://doi.org/10.4213/mzm10285

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English version:
Mathematical Notes, 2015, 97:2, 164–178

Bibliographic databases:

Document Type: Article
UDC: 517.98
Received: 19.03.2013
Revised: 08.06.2013

Citation: A. G. Baskakov, “Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces”, Mat. Zametki, 97:2 (2015), 174–190; Math. Notes, 97:2 (2015), 164–178

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. Yu. Duplischeva, “O differentsialnykh operatorakh i matritsakh vtorogo poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:1 (2015), 31–37  mathnet  crossref  elib
    3. M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. B. Antonevich, E. V. Panteleeva, “Well-Posed Boundary-Value Problems, Right Hyperbolicity, and Exponential Dichotomy”, Math. Notes, 100:1 (2016), 11–23  mathnet  crossref  crossref  mathscinet  isi  elib
    5. I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Siberian Math. J., 57:1 (2016), 145–154  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  isi  elib
    7. A. G. Baskakov, L. Yu. Kabantsova, I. D. Kostrub, T. I. Smagina, “Linear differential operators and operator matrices of the second order”, Differ. Equ., 53:1 (2017), 8–17  crossref  mathscinet  zmath  isi  scopus
    8. I. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v prostranstvakh Stepanova”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:2 (2017), 172–182  mathnet  crossref  elib
    9. A. A. Ryzhkova, “Garmonicheskii analiz periodicheskikh na beskonechnosti posledovatelnostei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 22–32  mathnet  crossref
    10. A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Russian Math. (Iz. VUZ), 61:10 (2017), 32–43  mathnet  crossref  isi
    11. L. Yu. Kabantsova, “Lineinye raznostnye uravneniya vtorogo poryadka v banakhovom prostranstve i rasscheplenie operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:3 (2017), 285–293  mathnet  crossref  elib
    12. I. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v odnorodnykh prostranstvakh”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 29–38  mathnet  crossref
    13. I. A. Trishina, “Pochti periodicheskie na beskonechnosti funktsii otnositelno podprostranstva integralno ubyvayuschikh na beskonechnosti funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:4 (2017), 402–418  mathnet  crossref  elib
    14. Baskakov A. Obukhovskii V. Zecca P., “Almost Periodic Solutions At Infinity of Differential Equations and Inclusions”, J. Math. Anal. Appl., 462:1 (2018), 747–763  crossref  mathscinet  zmath  isi  scopus
    15. Baskakov A.G., Kabantsova L.Yu., Smagina T.I., “Invertibility Conditions For Second-Order Differential Operators in the Space of Continuous Bounded Functions”, Differ. Equ., 54:3 (2018), 285–294  crossref  mathscinet  zmath  isi  scopus
    16. A. G. Baskakov, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Siberian Math. J., 59:2 (2018), 231–242  mathnet  crossref  crossref  isi  elib
    17. A. G. Baskakov, N. B. Uskova, “Fourier method for first order differential equations with involution and groups of operators”, Ufa Math. J., 10:3 (2018), 11–34  mathnet  crossref  isi
    18. A. G. Baskakov, V. E. Strukov, I. I. Strukova, “On the almost periodic at infinity functions from homogeneous spaces”, Probl. anal. Issues Anal., 7(25):2 (2018), 3–19  mathnet  crossref
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