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Fock-type spaces associated to higher-order Bessel operator

ABSTRACT In this paper we study the Fock-type space of analytic functions on the plane, invariant with respect to rotations of the plane by , with weight generated in a special way from the solutions of the higher-order Bessel equation. We give an explicit construction of the Bergman kernel for this space; and we prove that the operator of multiplication by is adjoint in this space to the higher-order Bessel operator. These instruments are used to investigate, in this new setting, some standard properties of operators in this space, including the basic properties of Toeplitz and Hankel operators, the uncertainty property and extremal functions for some operators.