On a class of diagonal operators in the spaces of analytic functions and its application

Authors

  • Yu. S. Linchuk

DOI:

https://doi.org/10.15407/dopovidi2014.03.025

Keywords:

analytic functions, application, diagonal operators

Abstract

Diagonal operators induced by the Taylor coefficients of hypergeometric functions and some properties of such operators in the spaces of functions analytic in arbitrary domains are investigated. The results are applied to study properties of the generalized Dunkl operator.

Downloads

References

Deters I. N., Seubert S. M. J. Math. Anal. Appl., 2007, 334, No. 2: 1209–1219. https://doi.org/10.1016/j.jmaa.2007.01.035

Linchuk N. E. Izv. vuzov. Matem., 1985, No. 5: 72–74 (in Russian).

Linchuk N. E., Linchuk S. S. Ukr. mat. zhurn., 2011, 63, No. 1: 61–68 (in Ukrainian).

Linchuk S. S. Diagonal operators in spaces of analytic functions and their applications. In: Current problems in function theory. Rostov-on-Don: Rostov. Gos. Univ., 1987: 118–121.

Bratishchev A. V. Dokl. RAN, 1999, 365, No. 1: 9–12 (in Russian).

Müller J. Complex variabl. Theory Appl., 1992, 18: 155–166.

Dimovski I. H. Convolutional calculus. Dordrecht: Kluwer, 1990. https://doi.org/10.1007/978-94-009-0527-6

Ben Salem N., Kallel S. Comment. Math. Univ. Carolin., 2004, 45, No. 4: 699–725.

Betancor J. J., Sifi M., Trimeche K. Acta Math. Hungar, 2005, 106, No. 1–2: 101–116. https://doi.org/10.1007/s10474-005-0009-1

Bratishchev A. V. Vestn. DGTU, 2009, 9, No. 2: 196–207 (in Russian).

Zabirova K. R., Napalkov V. V. Dokl. RAN, 2013, 449, No. 6: 632–634 (in Russian). https://doi.org/10.7868/S0869565213070074

Published

11.02.2025

How to Cite

Linchuk, Y. S. (2025). On a class of diagonal operators in the spaces of analytic functions and its application . Reports of the National Academy of Sciences of Ukraine, (3), 25–28. https://doi.org/10.15407/dopovidi2014.03.025