Displaying similar documents to “Invariant operators on function spaces on homogeneous trees”

A Paley-Wiener theorem on NA harmonic spaces

Francesca Astengo, Bianca di Blasio (1999)

Colloquium Mathematicae

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Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.

Harmonic analysis of spherical functions on S U ( 1 , 1 )

Y. Benyamini, Yitzhak Weit (1992)

Annales de l'institut Fourier

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Denote by L 1 ( K ∖ G / K ) the algebra of spherical integrable functions on S U ( 1 , 1 ) , with convolution as multiplication. This is a commutative semi-simple algebra, and we use its Gelfand transform to study the ideals in L 1 ( K ∖ G / K ) . In particular, we are interested in conditions on an ideal that ensure that it is all of L 1 ( K ∖ G / K ) , or that it is L 0 1 ( K ∖ G / K ) . Spherical functions on S U ( 1 , 1 ) are naturally represented as radial functions on the unit disk D in the complex plane. Using this representation, these results are applied to characterize...