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