A singular convolution equation in the space of distributions.
We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on If is a Schwartz class function we show that is supported in a ball of radius in if and only if for for all This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When we show that the two conditions for imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...
There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...
Mathematics Subject Classification: 44A40, 45B05The paper presents an abstract linear second kind Fredholm integral equation with degenerated kernel defined by means of the Bittner operational calculus. Fredholm alternative for mutually conjugated integral equations is also shown here. Some examples of solutions of the considered integral equation in various operational calculus models are also given.
In this paper we get an algebraic derivative relative to the convolution associated to the operator , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation