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A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on n

E. K. Narayanan, S. Thangavelu (2006)

Annales de l’institut Fourier

We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on n . If f ( z ) e 1 4 | z | 2 is a Schwartz class function we show that f is supported in a ball of radius B in n if and only if f × μ r ( z ) = 0 for r > B + | z | for all z n . This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 we show that the two conditions f × μ r ( z ) = μ r × f ( z ) = 0 for r > B + | z | imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...

A uniform estimate for quartile operators.

Christoph Thiele (2002)

Revista Matemática Iberoamericana

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...

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Wysocki, Hubert, Zellma, Marek (2005)

Fractional Calculus and Applied Analysis

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.

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