An optimization problem concerning multiplicative functions

Hilberdink, T. (2015) An optimization problem concerning multiplicative functions. Linear Algebra and its Applications, 485. pp. 289-304. ISSN 0024-3795 doi: 10.1016/j.laa.2015.07.005

Abstract/Summary

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0<f(p)<1, the solution is at a multiplicative point for all q≥1.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/50983
Identification Number/DOI	10.1016/j.laa.2015.07.005
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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