Let $\Delta $ be the Laplace-Beltrami operator on a Damek-Ricci space $ S $ corresponding
to the left-invariant Riemannian metric, with its $ L^ 2$-spectrum being the half line $(-\infty …

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's
problem: determining the optimal regularity of the initial condition f of the Schrödinger …

In this paper we study an extension problem for the Laplace-Beltrami operator on
Riemannian symmetric spaces of noncompact type and use the solution to prove Hardy-type …

In 1980, Roe proved that if a doubly-infinite sequence $\{f_k\} $ of functions on $\mathbb {R}
$ satisfies $ f_ {k+ 1}=(df_ {k}/dx) $ and $| f_ {k}(x)|\leq M $ for all $ k= 0,\pm 1,\pm 2,\cdots …

In this paper we extend classical Titchmarsh theorems on the Fourier–Helgason transform of
Lipschitz functions to the setting of Lp-space on Damek–Ricci spaces. As consequences …

In a recent paper by the authors, growth properties of the Fourier transform on Euclidean
space and the Helgason Fourier transform on rank one symmetric spaces of non-compact …

In this paper we prove that for λ∈ R∖{0} the Poisson transform P λ F of F∈ L 2 (K/M)
belongs to L 2,∞(G/K). This complements an earlier result of Lohoué and Rychener. Using …

We shall obtain inequalities for Fourier transform via moduli of continuity on NA groups.
These results in particular settle the conjecture posed in a recent paper by WO Bray and M …

We consider the rank one Riemannian symmetric spaces of noncompact type and their non-
symmetric generalization, namely the Damek-Ricci spaces. We show that the heat …

Dynamics of the heat semigroup in Jacobi analysis Page 1 J. Math. Anal. Appl. 391 (2012)
48–56 Contents lists available at SciVerse ScienceDirect Journal of Mathematical Analysis and …