On Biorthogonalization of a Dirichlet SystemOver a Finite Interval

Author(s)

On Biorthogonalization of a Dirichlet SystemOver a Finite Interval Mher Martirosyan

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.

DOI: 10.52737/18291163-2019.11.4-1-9 Armenian Journal of Mathematics, 11(4) 1-9

Download PDF

Keywords

Dirichlet Polynomials, Biorthogonal Systems, Blaschke Prod-uct, Gram Matrix, Bernstein-Type Inequality

Check for updates

Share

Contact admin with any questions, comments or concerns

[email protected]