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On the applicability of differential operators of infinite order with respect to the $q$ -derivative
Linchuk Stepan Stepanovich 1
1 Chernivtsi National University named after Yuriy Fedkovych, Chernivtsi, 58002, Ukraine
Keywords: differential operators, the $q$ -derivative
Abstract
We obtain necessary and sufficient conditions for the applicability of differential operators of infinite order with respect to the $q$ -derivative to the spaces of analytic functions in circular domains.
References

[1] F. H. Jackson On $q$-functions and a certain difference operator // Trans. Roy. Soc. Edin. – 1908. – №46. – P. 253-281.

[2] G. Bangerezako An Introduction to $q$-Difference Equations. – Preprint, Miramare-Trieste. 2011. – 79 p.

[3] Yu.F. Korobeinik Shift Operators on Numerical Families. - Rostov-on-Don: Izd-vost Rost.un-ta. - 1983. - 155 p.

[4] S.S. Linchuk On the applicability of differential and integral operators of infinite order // Dep. in VINITI 13 April 1982, №1799-82. - Chernivtsi, 1982. - 25 p.

[5] S. S. Linchuk On the representation of linear continuous operators acting in spaces of analytic functions of many variables.- 1984. -35. - №5. - P.721-727.

[6] I. Rajchinov On some commutation properties of the algebra of the linear operators acting in spaces of analytic functions I. // God. Vissh. Uchebn. Zaved., Prilozhna Mat. – 1979. – 15 . №3. – P. 27-40.

[7] S.S. Linchuk, Y.S. Linchuk Operators in spaces of analytical functions. - In: Ruta, 2011. - 147 p.

Cite
ACS Style
Linchuk, S.S. On the applicability of differential operators of infinite order with respect to the $q$ -derivative. Bukovinian Mathematical Journal. 2016, 1
AMA Style
Linchuk SS. On the applicability of differential operators of infinite order with respect to the $q$ -derivative. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style
Stepan Stepanovich Linchuk. 2016. "On the applicability of differential operators of infinite order with respect to the $q$ -derivative". Bukovinian Mathematical Journal. 1 no. 3-4.
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