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Displaying 1381 – 1400 of 2299

On the Haagerup inequality and groups acting on ${\tilde{A}}_{n}$ -buildings

Alain Valette (1997)

Annales de l'institut Fourier

Let $Γ$ be a group endowed with a length function $L$ , and let $E$ be a linear subspace of $C Γ$ . We say that $E$ satisfies the Haagerup inequality if there exists constants $C, s > 0$ such that, for any $f \in E$ , the convolutor norm of $f$ on $ℓ^{2} (Γ)$ is dominated by $C$ times the $ℓ^{2}$ norm of $f (1 + L)^{s}$ . We show that, for $E = C Γ$ , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on $Γ$ . If $L$ is a word length function on a finitely generated group $Γ$ , we show that,...

On the Hausdorff-Young Theorem for Amalgams.

John J.F. Fournier (1983)

Monatshefte für Mathematik

On the Hausdorff-Young theorem for commutative hypergroups

Sina Degenfeld-Schonburg (2013)

Colloquium Mathematicae

We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in $L^{p} (K, m)$ and $L^{p} (K ̂, π)$ respectively, where 1 ≤ p ≤ 2. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space K̂ is in general not a hypergroup itself.

On the image of a generalized $d$ -plane transform on $ℝ^{n}$ .

Symeonidis, Elevtherios (1999)

Journal of Lie Theory

On the inverse Abel transforms for certain Riemannian symmetric spaces of rank 2.

Fuliu Zhu (1996)

Mathematische Annalen

On the Levy-Chintschin formula on locally compact maximally almost periodic groups.

Eberhard Siebert (1977)

Mathematica Scandinavica

On the Multiresolution analysis of abstract Hilbert spaces

Theodoros Stavropoulos, Manos Papadakis (1998)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On the notion of virtual amenability for groups

Larry Baggett (1988)

Colloquium Mathematicae

On the o-Spektrum of Regular Operators and the Spectrum of Measures.

Wolfgang Ardendt (1981)

Mathematische Zeitschrift

On the Paley-Wiener theorem.

Michael Cowling (1986)

Inventiones mathematicae

On the Plancherel Measure for Linear Lie Groups of Rank One.

Roberto J. Miatello (1979)

Manuscripta mathematica

On the product formula on noncompact Grassmannians

Piotr Graczyk, Patrice Sawyer (2013)

Colloquium Mathematicae

We study the absolute continuity of the convolution $δ_{e^{X}}^{♮} * δ_{e^{Y}}^{♮}$ of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of...

On the product theory of singular integrals.

Alexander Nagel, Elias M. Stein (2004)

Revista Matemática Iberoamericana

We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...

On the projectivity and flatness of some group modules

Gerhard Racher (2010)

Banach Center Publications

In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.

On the Property P... of Locally Compact Groups

A. Derighetti (1971)

Commentarii mathematici Helvetici

On the Proportionality of Covolumes of Discrete Subgroups.

J. Rohlfs, G.A. Margulis (1986)

Mathematische Annalen

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

Jelassi, M., Rachdi, L. (2004)

Fractional Calculus and Applied Analysis

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

On the range of the Fourier transform connected with Riemann-Liouville operator

Lakhdar Tannech Rachdi, Ahlem Rouz (2009)

Annales mathématiques Blaise Pascal

We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator $ℛ_{α}, α \geq 0$ and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.

On the Relation between Amenability of Locally Compact Groups and the Norms of Convolution Operators.

Christian Berg, Jens Peter Reuss Christensen (1974)

Mathematische Annalen

On the relation between Gaussian measures and convolution semigroups of local type.

Christian Berg (1975)

Mathematica Scandinavica

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