2019
Том 71
№ 11

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A generalization of the rogosinski-rogosinski theorem

Dekanov S. Ya., Mikhalin G. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 52 (2000), no. 2, pp 249-259.

Citation Example: Dekanov S. Ya., Mikhalin G. A. A generalization of the rogosinski-rogosinski theorem // Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 220-227.

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