On polyconvolutions generated by the Hankel transform (Q1889685)

The author introduces the so-called polyconvolution operators, which are associated with the Hankel transform. The existence and factorization properties for these generalized convolutions are proved. It involves Hankel's transforms of different order. By using the differential properties for the Hankel transform the author constructs more convolutions of this type. As applications these operators are involved to solve new classes of convolution integral and integro-differential equations and also systems of such equations.