V. V. Napalkov jr., A. A. Nuyatov, “Abel — Goncharov problem in kernel of convolution operator”, Ufimsk. Mat. Zh., 2025, Volume 17, Issue 4,Pages <nobr>74

Abel — Goncharov problem in kernel of convolution operator

V. V. Napalkov jr.^a, A. A. Nuyatov^b

^a Institute of Mathematics, Ufa Federal Research Center, RAS, Chernyshevsky str. 112, 450008, Ufa, Russia
^b Nizhny Novgorod State Technical University named after R.E. Alekseev, Minin str. 24, 603155, Nizhny Novgorod, Russia

Abstract: In the work we prove that the multiple interpolation problem is solvable, and as a corollary, the same for the Abel — Goncharov problem in the kernel of a convolution operator, when the zero sequence of the characteristic function of the convolution operator and the nodes, which are zeros of an entire function, are located in some angles in the complex plane and the nodes are multiple.

Keywords: multiple interpolation, Abel — Goncharov problem, convolution operator, entire functions.

UDC: 517.98

MSC: 46A13, 30D20

Received: 04.02.2025