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
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
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
Language eng
Relation http://armjmath.sci.am/index.php/ajm/article/view/268/145
Rights Copyright (c) 2019 Armenian Journal of Mathematics

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