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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].

A Paley-Wiener theorem on NA harmonic spaces

Francesca Astengo, Bianca di Blasio (1999)

Colloquium Mathematicae

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.

A Qualitative Uncertainty Principle for Certain Locally Compact Groups.

E. KANIUTH, S. Echterhoff, A. Kumar (1991)

Forum mathematicum

A Remark on Continuity of Translation Invariant Functionals on L... (G) for Compact Lie Groups G.

Jaroslaw Krawczyk (1990)

Monatshefte für Mathematik

Algèbres $A_{p}$ et convoluteurs de $L^{p}$

Pierre Eymard (1969/1970)

Séminaire Bourbaki

Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

Nico Spronk (2010)

Banach Center Publications

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, $L^{- 1} (G)$ and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for $L^{- 1} (G)$ and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...

An analogue of Hardy's theorem for the Heisenberg group

S. Thangavelu (2001)

Colloquium Mathematicae

We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.

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A characterization of bi-invariant Schwartz space multipliers on nilpotent Lie groups

A Heat Semigroup Version of Bernstein's Theorem on Lie Groups.

A new group algebra and lacunary sets in discrete noncommutative groups

A Paley-Wiener theorem for nilpotent Lie groups. (Un théorème de Paley-Wiener pour les groupes de Lie nilpotents.)

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

A Paley-Wiener theorem on NA harmonic spaces

A Qualitative Uncertainty Principle for Certain Locally Compact Groups.

A Remark on Continuity of Translation Invariant Functionals on L... (G) for Compact Lie Groups G.

Algèbres $A_{p}$ et convoluteurs de $L^{p}$

Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

An analogue of Hardy's theorem for the Heisenberg group

An inversion formula for weighted orbital integrals

An $L^{p}$ - $L^{q}$ version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups.

Analyse harmonique sur les groupes algébriques complexes : formule de Plancherel

Approximation of double coset spaces

Approximation Theory, Absolute Convergence, and Smoothness of Random Fourier Series on Compact Lie Groups.

Base d'ondelettes sur les groupes de Lie stratifiés

Bochner's theorem for finite-dimensional conelike semigroups.

Characterization of perfect involution groups.

Continuity of Operators Commuting with Translations for Compact Groups.

Currently displaying 1 – 20 of 98