Uniform convergence of sine integral-series - Kórus Péter; Krasniqi Xhevat Z.; Szal Bogdan (2022)
In this paper we define the class GMSF(alpha, beta, gamma) of General Monotone Sequence of Functions with majorants alpha, beta, gamma : (R) over bar (2)(+) -> (R) over bar (+), (R) over bar (+) := [0, infinity). For a sequence of admissible functions {f(k)(t)}(k=1)(infinity) subset of C belonging to this class we find necessary and sufficient conditions under which the sine integral-seriesintegral(infinity)(0)Sigma(k=1) f(k)(t) sin ku sin tv dtconverges in the regular sense uniformly in (u, v) is an element of <(R)over bar(+)(2).
Keywords: Matematika