On the almost periodic functions in the sense of Levitan

• Autorzy: Michałowicz A. , Stoiński S.
• Języki publikacji: EN

Abstrakty

EN

In this note we present some theorems on the superposition of an (NVp)-almost periodic (a.p. for short) function, a μ-a.p. function and an (Nμ)-a.p. function. Moreover, we prove a theorem on the bounded primary function of an (NS^p)-a.p. function. Finally, we prove that the inverse of a V_p-a.p. function is (NV_p)-a.p.

Słowa kluczowe

EN

almost periodic functions; superposition; primary function; lebesgue measure

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 2
• Strony: 149--159
• Opis fizyczny: bibliogr. 12 poz.

Twórcy

autor

Michałowicz A.

autor

Stoiński S.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University Umultowska 87, 61-614 Pozna´n, Poland,

Bibliografia

• [1] M. Adamczak, On compactness of C(n)-almost periodic functions, Demonstr. Math. Vol.32 No 2 (1999), 385-393.
• [2] A. S. Besicovitch, Almost periodic functions, Cambridge 1932.
• [3] H. Bohr, Zur Theorie der fastperiodischen Funktionen, I. Teil Eine Verallgemeinerung der Theorie der Fourierreihen, Acta math. 45 (1925), 29-127; II. Teil Zusammenhang der fastperiodischen Funktionen mit Funktionen von unendlichvielen Variablen; gleichm¨assige Approximation durch trigonometrische Summen, Acta math. 46 (1925), 101-214.
• [4] C. Corduneanu, Almost Periodic Functions, Chelsea Publishing Co., New York 1989.
• [5] B. M. Levitan, Almost periodic functions, Moscow 1953 (in Russian) .
• [6] S. Stoi´nski, Real-valued functions almost periodic in variation, Funct. Approximatio, Comment. Math. 22 (1993), 141-148.
• [7] S. Stoiński, Almost periodic functions in the Lebesgue measure, Commentat. Math. 34 (1994), 189-198.
• [8] S. Stoiński, Real-valued functions almost periodic in p-variation, Fasc. Math. 26 (1996), 155-162.
• [9] S. Stoiński, N-almost periodic in the sense of variation functions, Commentat. Math. 41 (2001), 195-202.
• [10] S. Stoiński, A note on N-almost periodic functions and (NI)-almost periodic functions, Commentat. Math. 44 (2) (2004), 199-204.
• [11] S. Stoiński, On superposition of almost periodic functions, International Journal of Evolution Equations 1 No 2 (2005), 145-151.
• [12] S. Stoiński, On the almost periodicity of the superposition of functions, (in the press).