Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Discrete Biorthogonal Systems and Rational Interpolation in the Hardy Space of Unit Disc and Upper Half Plane"

Pap, Margit

Recently Fridli and Schipp introduced a discrete biorthogonal system in the Hardy space of the unit disc. Starting from their results we introduce the dual system of the Malmquist-Takenaka complex orthonormal system on the upper half-plane, For both cases, the discrete scalar products are defined over certain nodal points in the unit disc and upper half-plane respectively. For these nodal points, we proved similar equilibrium conditions as it was proved previously for the discrete orthogonal system on the unit circle and on the real line. Using these biorthogonal systems we introduce new rational interpolation operators and we study their properties.
http://univie.ac.at/projektservice-mathematik/e/talks/strobl22_Pap_2022-04_Birtohogonal_system_Pap_Abstract_Strobl2022.pdf

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