A Paley-Wiener theorem on NA harmonic spaces

Francesca Astengo; Bianca di Blasio

Displaying similar documents to “A Paley-Wiener theorem on NA harmonic spaces”

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

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The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.

A Paley-Wiener theorem for step two nilpotent Lie groups.

Sundaram Thangavelu (1994)

Revista Matemática Iberoamericana

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It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].

Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains

Ewa Damek, Andrzej Hulanicki (2000)

Studia Mathematica

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Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Michael Cowling, Saverio Giulini, Andrzej Hulanicki, Giancarlo Mauceri (1994)

Studia Mathematica

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We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for $L^{1} (A N),$ but also for $L^{p} (A N)$ , where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.

Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups

Ewa Damek (1988)

Studia Mathematica

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Bochner and Schoenberg theorems on symmetric spaces in the complex case

Piotr Graczyk, Jean-Jacques Lœb (1994)

Bulletin de la Société Mathématique de France

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Invariant systems of conjugate harmonic functions associated with compact Lie groups

Ronald Coifman, Guido Weiss (1972)

Studia Mathematica

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Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms

Ewa Damek (1997)

Colloquium Mathematicae

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Invariant harmonic unit vector fields on Lie groups

J. C. González-Dávila, L. Vanhecke (2002)

Bollettino dell'Unione Matematica Italiana

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We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine...