A generalization of the rogosinski-rogosinski theorem

  • S. Ya. Dekanov
  • G. A. Mikhalin


We establish necessary and sufficient conditions for numerical functions αj(x), jN, xX, under which the conditions K(f j K(f 1) ∀j≥2 and \(\mathop {\lim }\limits_{U_r } \sum\nolimits_{j = 1}^\infty {\alpha _j (x)f_j (x) = a} \) yield \(\mathop {\lim }\limits_{U_r } f_1 (x) = a.\) The functions fj(x) are uniformly bounded on the set X and take values in a boundedly compact space L, and K(fj) is the kernel of the function fj. The well-known Rogosinski-Rogosinski theorem follows from the proved statements in the case where X = N, α j (x) ≡ αj, and the space L is the m-dimensional Euclidean space.
How to Cite
Dekanov, S. Y., and G. A. Mikhalin. “A Generalization of the Rogosinski-Rogosinski Theorem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 52, no. 2, Feb. 2000, pp. 220-7, https://umj.imath.kiev.ua/index.php/umj/article/view/4410.
Research articles