Object structure

Journal or Publication Title:

Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես

Date of publication:

2019

Volume:

11

Number:

4

ISSN:

1829-1163

Additional Information:

Electronic Open Access Publication of the National Academy of Sciences of Armenia

Title:

On Biorthogonalization of a Dirichlet System Over a Finite Interval

Creator:

Mher Martirosyan ; Davit Martirosyan

Subject:

Functions of a complex variable ; Approximations and expansions ; Fourier analysis

Coverage:

1-9

Abstract:

Ultimately aiming to estimate Dirichlet polynomials, a representation problem for special biorthogonal systems of exponentials is explored in $L^2(0,a)$. If $a=+\infty$, a method of construction of such systems through suitable Blaschke products is known, but the method ceases to operate when $a$ is finite. It turns out that the Blaschke product cannot be even adjusted to maintain the old method for the new situation. The biorthogonal system is then represented by a single determinant of a modified Gram matrix of the original system. Bernstein-type inequalities for Dirichlet polynomials and their higher order derivatives are established. The best constants and extremal polynomials are obtained in terms of the Gram matrix.

Publisher:

National Academy of Sciences of Armenia

Date created:

2019-04-19

Type:

Article

Format:

pdf

Location of original object:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան