On Biorthogonalization of a Dirichlet System Over a Finite Interval

Authors

  • Mher Martirosyan Yerevan State University
  • Davit Martirosyan American University of Armenia

Keywords:

Dirichlet Polynomials, Biorthogonal Systems, Blaschke Product, Gram Matrix, Bernstein-Type Inequality

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.

Downloads

Published

2019-04-17

How to Cite

Martirosyan, M., & Martirosyan, D. (2019). On Biorthogonalization of a Dirichlet System Over a Finite Interval. Armenian Journal of Mathematics, 11(4), 1–9. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/268