### On Biorthogonalization of a Dirichlet System Over a Finite Interval

#### Armenian Journal of Mathematics

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 Field Value Title On Biorthogonalization of a Dirichlet System Over a Finite Interval Creator Martirosyan, Mher Martirosyan, Davit Subject Dirichlet Polynomials Biorthogonal Systems Blaschke Product Gram Matrix Bernstein-Type Inequality 30B50 41A17 42C05 Description 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 2019-04-17 Type info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peer-reviewed Article Format application/pdf Identifier http://armjmath.sci.am/index.php/ajm/article/view/268 Source Armenian Journal of Mathematics; Vol. 11 No. 4 (2019): On Biorthogonalization of a Dirichlet System Over a Finite Interval; 1-9 1829-1163 Language eng Relation http://armjmath.sci.am/index.php/ajm/article/view/268/145 Rights Copyright (c) 2019 Armenian Journal of Mathematics