ON THE MATRIX NORMS OF A GCD RELATED MATRIX


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Altinisik E.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.11, no.4, pp.635-646, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.7153/mia-11-53
  • Title of Journal : MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Page Numbers: pp.635-646

Abstract

In this paper we investigate the matrix norms of a GCD related matrix, i.e., (S-f) = (f (i,j)/(i(r)j(r))) for multiplicative arithmetical functions f. In particular, we obtain upper bounds for the lp norms of (S-f) for f = phi, sigma alpha and psi in terms of infinite prime products. Furthermore, we give lower and upper bounds for these infinite prime products by using particular norm inequalities.