On Biorthogonalization of a Dirichlet System Over a Finite Interval

Armenian Journal of Mathematics

View Publication Info
 
 
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
 

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