Abstract:
We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory.
Key words:
Banach space, Banach algebra, slowly varying at infinity functions, periodic at infinity functions, Fourier series, modulus of continuity.
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: Russian
Citation:
I. I. Strukova, “About harmonic analysis of periodic at infinity functions”, Izv. Saratov Univ. Math. Mech. Inform., 14:1 (2014), 28–38
\Bibitem{Str14}
\by I.~I.~Strukova
\paper About harmonic analysis of periodic at infinity functions
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 1
\pages 28--38
\mathnet{http://mi.mathnet.ru/isu483}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-1-28-38}
\elib{https://elibrary.ru/item.asp?id=21510770}
Linking options:
https://www.mathnet.ru/eng/isu483
https://www.mathnet.ru/eng/isu/v14/i1/p28
This publication is cited in the following 7 articles:
I. I. Strukova, “On Some Properties of Functions Almost Periodic at Infinity from Homogeneous Spaces”, J Math Sci, 263:5 (2022), 643
Vysotskaya I.A., Strukova I.I., “The Research of Some Classes of Almost Periodic At Infinity Functions”, Izv. Sarat. Univ. Novaya Ser.-Mat. Mekhan. Inform., 21:1 (2021), 4–14
V. E. Strukov, I. I. Strukova, “Garmonicheskii analiz medlenno menyayuschikhsya na beskonechnosti polugrupp operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 19:2 (2019), 152–163
I. I. Strukova, “O nekotorykh svoistvakh pochti periodicheskikh na beskonechnosti funktsii iz odnorodnykh prostranstv”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 47–56
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
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
I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Siberian Math. J., 57:1 (2016), 145–154
Citation in format AMSBIB
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