Universality Properties of a Double Series by the Generalized Walsh System. (22nd April 2013)

• Record Type: Journal Article
• Authors: Episkoposian, Sergo A.
• Other Names: Robert Frédéric Academic Editor.
• Is Part Of: International journal of analysis. Volume 2013(2013)
• Publication Date: 2013-04-22
• Subjects: Mathematical analysis -- Periodicals; 515.05
• DOI: 10.1155/2013/424686
• Languages: English
• ISSNs: 2314-498X

Abstract

Abstract : We consider a question on existence of a double series by the generalized Walsh system, which is universal in weighted L μ 1 [ 0, 1 ] 2 spaces. In particular, we construct a weighted function μ ( x, y ) and a double series by generalized Walsh system of the form ∑ n, k = 1 ∞ ‍ c n, k ψ n ( x ) ψ k ( y ) with the ∑ n, k = 1 ∞ ‍ | c n, k | q < ∞ for all q > 2, which is universal in L μ 1 [ 0, 1 ] 2 concerning subseries with respect to convergence, in the sense of both spherical and rectangular partial sums.