Horocyclic Radon transform on Damek-Ricci space

• Autorzy: Abouelaz A. , El Fourchi O.
• Języki publikacji: EN

Abstrakty

EN

We study the horocyclic Radon transform, defined in [5], of Damek-Ricci space. This transform R is obtained by integration over an orbitals family of NA space. We establish a Plancherel's formula for this transform. In particular, we characterize the range of horocyclic Radon transform of certain subspace of [L^2] ( NA, dx). The operators R and R*, where R* is the dual Radon transform of R, are inverted by a differential operator with constant coefficients (if dim NA is odd), or an integro-differential operator (if dim NA is even). The inversion formulas obtained are similar to the inversion formulas in symmetric space of noncompact type (see [7], [18], [19]). Also, we prove a radial Paley-Wiener-Schwartz's theorem for Damek-Ricci space.

Słowa kluczowe

EN

Damek-Ricci space; Paley-Wiener theorems; Plancherel's formula; Poisson kernel; radon transform

PL

jądro Poissona; przestrzeń Damek-Ricci; transformata Radona; twierdzenie Paley'a-Wienera; wzór Plancherela

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 2
• Strony: 107--140
• Opis fizyczny: Bibliogr. 27 poz.,

Twórcy

autor

Abouelaz A.

autor

El Fourchi O.