Almost periodic measures with respect to different metrics

S.Yu.Favorov; Ye.Yu.Kolbasina

We study measures on $\mathbb{R}^k$ that almost periodic in the weak sense and in the sense of Sodin-Tsirelson's metric. Also, we describe a connection between these classes of almost periodic measures.

1. Corduneanu C. Almost Periodic Functions, Interscience Publishers, New-York-London-Sydney, 1968.

2. Favorov S., Kolbasina Ye. Almost periodic discrete sets, Journal of Mathematical Physics, Analysis, Geometry, 6 (2010), №1, 1-14.

3. Favorov S., Rashkovskii A., Ronkin L. Almost periodic divisors in a strip, J. Anal. Math. 74 (1998), 325-345.

4. Kantorovich L.V. and Akilov G.P. Functional analysis in normed spaces (3rd edition). Nauka, Moscow, 1984. (in Russian) Engl. transl. of the 2nd edition: Pergamon Press, Oxford-Elmsford, N.Y., 1982.

5. Kolbasina Ye.Yu. On the property of discrete set in $\mathbb{R}^k$, Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh. 2008, № 826, 52-66 (Russian).

6. Niculescu C.P., Persson L.-E. Convex functions and their applications. A contemporary approach, Springer, 2006.

7. Ronkin L.I. Almost periodic distributions and divisors in tube domains, Zap. Nauchn. Sem. POMI 247 (1997), 210-236 (Russian).

8. Sodin M., Tsirelson B., Uniformly spread measures and vector fields, arXiv: 0801.2505.

	Almost periodic measures with respect to different metrics
Author	S.Yu.Favorov, Ye.Yu.Kolbasina Sergey.Ju.Favorov@univer.kharkov.ua, kvr_jenya@mail.ru Department of Mechanics and Mathematics, Kharkov National University,61077 Kharkov, Svobody sq. 4, Ukraine
Abstract	We study measures on $\mathbb{R}^k$ that almost periodic in the weak sense and in the sense of Sodin-Tsirelson's metric. Also, we describe a connection between these classes of almost periodic measures.
Keywords	almost periodic measure, weak sense, Sodin-Tsirelson's metric
DOI	doi:10.30970/ms.33.2.125-138
Reference	1. Corduneanu C. Almost Periodic Functions, Interscience Publishers, New-York-London-Sydney, 1968. 2. Favorov S., Kolbasina Ye. Almost periodic discrete sets, Journal of Mathematical Physics, Analysis, Geometry, 6 (2010), №1, 1-14. 3. Favorov S., Rashkovskii A., Ronkin L. Almost periodic divisors in a strip, J. Anal. Math. 74 (1998), 325-345. 4. Kantorovich L.V. and Akilov G.P. Functional analysis in normed spaces (3rd edition). Nauka, Moscow, 1984. (in Russian) Engl. transl. of the 2nd edition: Pergamon Press, Oxford-Elmsford, N.Y., 1982. 5. Kolbasina Ye.Yu. On the property of discrete set in $\mathbb{R}^k$, Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh. 2008, № 826, 52-66 (Russian). 6. Niculescu C.P., Persson L.-E. Convex functions and their applications. A contemporary approach, Springer, 2006. 7. Ronkin L.I. Almost periodic distributions and divisors in tube domains, Zap. Nauchn. Sem. POMI 247 (1997), 210-236 (Russian). 8. Sodin M., Tsirelson B., Uniformly spread measures and vector fields, arXiv: 0801.2505.
Pages	125-138
Volume	33
Issue	2
Year	2010
Journal	Matematychni Studii
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