# On Biorthogonalization of a Dirichlet System Over a Finite Interval

Martirosyan, Mher and Martirosyan, Davit (2019) On Biorthogonalization of a Dirichlet System Over a Finite Interval. Armenian Journal of Mathematics, 11 (4). pp. 1-9. ISSN 1829-1163

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## 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.

Item Type: Article 30-xx Functions of a complex variable41-xx Approximations and expansions42-xx Fourier analysis 842 Professor Anry Nersesyan 19 Apr 2019 22:58 19 Apr 2019 22:58

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