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In this article we give the definition and some properties of unbounded almost periodic functions in Hausdorff metric. Moreover, we examine almost periodicity of the inverse of a generalized trigonometric polynomial of constant sign.
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Czasopismo
Rocznik
Tom
Strony
17--22
Opis fizyczny
Bibliogr. 14 poz.
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autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland
Bibliografia
- [1] H. Bohr, Zur Theorie der fastperiodischen Funktionen, I Teil: Eine Verallgemeinerung der Theorie der Fourierreihen, Acta math. 45 (1925), 29–127.
- [2] A. S. Džafarov, G. M. Gasanov, Almost periodic functions with respect to the Hausdorff metric and some of their properties, Izv. Akad. Nauk Azerbaĭdžan. SSR, Ser. Fiz.-Techn. Mat. Nauk, No 1 (1977), 57–62 (in Russian).
- [3] F. Hausdorff, Grndzüge der Magenlehre, Leipzig, 1914.
- [4] B. M. Levitan, Almost Periodic Functions, Moscow, 1953 (in Russian) .
- [5] B. Sendov, Hausdorff Approximation, Kluwer Acad. Publ., 1990.
- [6] B. Sendov, B. Penkov, The "-entropy and the "-capacity of the space of continuous functions, B˘ulgar. Akad. Nauk. Izv. Mat. Inst. 6 (1962), 27–50 (in Bulgarian).
- [7] B. Sendov, V. A. Popov, On certain properties of the Hausdorff metric, Mathematica (Cluj) 8 (31) (1966), 163–172 (in Russian).
- [8] S. Stoiński, H-almost periodic functions, Funct. Approx. Comment. Math. 1 (1974), 113–122.
- [9] S. Stoiński, A connection between H-almost periodic functions and almost periodic functions of other types, Funct. Approx. Comment. Math. 3 (1976), 205–223.
- [10] S. Stoiński, Almost periodic functions in the Lebesgue measure, Ann. Soc. Math. Pol., Ser. I, Comment. Math. 34 (1994), 189–198.
- [11] S. Stoiński, A note on N-almost periodic functions and (NI)-almost periodic functions, Ann. Soc. Math. Pol., Ser. I, Comment. Math. 44(2) (2004), 199–204.
- [12] S. Stoiński, On superposition of almost periodic functions, Int. Journ. Evol. Equat. Vol. 1, No 2 (2005), 145–151.
- [13] S. Stoiński, On the almost periodicity of the superposition of functions, Int. Journ. Evol. Equat. Vol. 2, No 4 (2008), 333–342.
- [14] S. Stoiński, Almost Periodic Functions, Wyd. Nauk. UAM, Poznan, 2008 (in Polish).
Typ dokumentu
Bibliografia
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