On Biorthogonalization of a Dirichlet System Over a Finite Interval


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


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


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.




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