Armenian Journal of Mathematics, 11(4)
2019; 1–9
Shared with The Gufo

On Biorthogonalization of a Dirichlet SystemOver a Finite Interval

Mher Martirosyan*, Davit Martirosyan

Received: 2024-12-11 · Published: 2019-04-19

© 2019 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
Shared article.
Original title
On Biorthogonalization of a Dirichlet SystemOver a Finite Interval
Authors
Mher Martirosyan, Davit Martirosyan
Source journal
Armenian Journal of Mathematics, 11(4)
Published
2019-04-19
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2019.11.4-1-9

Abstract

Ultimately aiming to estimate Dirichlet polynomi-als, a representation problem for special biorthogonal systems ofexponentials is explored inL2(0,a). Ifa= +∞, a method ofconstruction of such systems through suitable Blaschke productsis known, but the method ceases to operate whenais finite.It turns out that the Blaschke product cannot be even ad-justed to maintain the old method for the new situation. Thebiorthogonal system is then represented by a single determinantof a modified Gram matrix of the original system. Bernstein-type inequalities for Dirichlet polynomials and their higher or-der derivatives are established. The best constants and extremalpolynomials are obtained in terms of the Gram matrix.
1 / ? 100% Open in new tab Download Cite

Loading the full text…

Download Follow Updates