Let G be an arbitrary starlike symmetric domain of the complex plane with respect to the origin. By H0(G)>H0(G)H0(G) denote the space of all even analytic functions in G equipped with the topology of compact convergence. We establish the conditions of equivalence of the Bessel operator to the square of differentiation in the space H0(G)>H0(G)H0(G).

Delsarte J. Sur certaines transformations fonctionnelles relative aux equations linearaires aux derivees partielles du second ordre // C. R. Acad. Sci. Paris. – 1938. – 206. – P. 1780–178

2 Trimeche K. Transformation integrale de Weyl et theorem de Paley-Wiener associations a un operator differentiel singulier sur (0,∞) // J. Math. Pures Appl. – 1981. – 60. – P. 51–98.

Berezovskaya G.M., Berezovsky N.I. Description of isomorphisms of the space of holomorphic functions, permutations with multiple multiplication //Ukr.matem.zhurn.–1984.–36.–№5.–C.611–615.

Dimovski I.H. Convolutional Calculus. Kluwer, Dordrecht. - 1990. - 208 p.

Linchuk Yu.S. A single class of diagonal operators in spaces of analytic functions and its application // Dop. NAS of Ukraine. – 2014. – No. 3. - S. 25–28.

Linchuk Yu.S. Generalized Dunkl–Opdam operator and its properties in the spaces of analytic functions in domains // J. Math. Sci. – 2017. – 220. – No. 1. – P. 1–14.

Tsarkov M.Yu. Isomorphisms of some analytic spaces, permutational with the degree of the differentiation operator // Theory of functions, functional analysis and their applications: Rep. science Sat. - Kh.: Khark Publishing House. University, 1970. – Issue 11. - S. 86-92.

Belhadj M., Betancor J.J. Hankel convolution operators on entire functions and distributions // J. Math. Anal. Appl. – 2002. – 276. – №1. – P. 40-63.