On the Dirichlet matrix operators in sequence spaces

Volume 44 / 2017

Artur Sowa Applicationes Mathematicae 44 (2017), 185-196 MSC: 42C20, 47B99, 65T99, 65R32. DOI: 10.4064/am2328-4-2017 Published online: 7 July 2017

Abstract

We study the analytic properties of certain special operators, referred to as D-matrix operators, which arise naturally from classical Dirichlet series. There are a number of incentives for this work, including the applicability of D-matrix operators to signal processing via fast computational algorithms. It was observed in a prior publication that certain types of D-matrix operators are continuous in $\ell _2$ (Sowa 2013). In this work the focus is on a complementary case that arises in relation to the special D-matrix associated with Riemann’s zeta function, and on its continuity properties in suitable Hilbert and Banach sequence spaces.

Authors

  • Artur SowaDepartment of Mathematics and Statistics
    University of Saskatchewan
    106 Wiggins Road
    Saskatoon, SK S7N 5E6, Canada
    e-mail

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