On the unconditional bases of cores generated by differential equations of the second order

Levchuk, VN
Dopov. Nac. akad. nauk Ukr. 2017, 3:3-7
https://doi.org/10.15407/dopovidi2017.03.003
Section: Mathematics
Language: Russian
Abstract: 

We obtain the necessary and sufficient conditions of unconditional basicity of functions that are solutions of second-order equations (Bessel-type), and the spectral parameter belongs to a discrete set coinciding with the zeros of an entire function of the exponential type.

Keywords: basicity, Bernstein class, Bessel equation, Hilbert space, operator, real function, unconditional basis
References: 
  1. Gudreev, G. M. & Levchuk, V. N. (2015). Description of unconditional bases formed by values of the Dunkl kernels. Funkts. analiz i ego pril., 49, Iss. 1, pp. 79-82 (in Russian). doi: https://doi.org/10.4213/faa3176; Funct. Anal. Its Appl., 49, Iss. 1, pp. 64-66. doi: https://doi.org/10.1007/s10688-015-0085-0.
  2. Gubreev G.M. (2014). Selected works. Dnipropetrovsk: Serednyak T.K. (in Russian).
  3. Akhieser N.I. (1965). Lectures on the approximation theory. Moscow: Nauka (in Russian).