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Displaying 121 – 136 of 136

Unitary Representations of a Semi-Direct Product of Lie Groups on ...-Cohomology Spaces.

I. SATAKE (1970/1971)

Mathematische Annalen

Vanishing of the first reduced cohomology with values in an $L^{p}$ -representation

Romain Tessera (2009)

Annales de l’institut Fourier

We prove that the first reduced cohomology with values in a mixing $L^{p}$ -representation, $1 < p < \infty$ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced $ℓ^{p}$ -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced $L^{p}$ -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also...

Volume of spheres in doubling metric measured spaces and in groups of polynomial growth

Romain Tessera (2007)

Bulletin de la Société Mathématique de France

Let $G$ be a compactly generated locally compact group and let $U$ be a compact generating set. We prove that if $G$ has polynomial growth, then ${(U^{n})}_{n \in ℕ}$ is a Følner sequence and we give a polynomial estimate of the rate of decay of $\frac{μ (U^{n + 1} ∖ U^{n})}{μ (U^{n})} .$ Our proof uses only two ingredients: the doubling property and a weak geodesic property that we call Property (M). As a matter of fact, the result remains true in a wide class of doubling metric measured spaces including manifolds and graphs. As an application, we obtain a $L^{p}$ -pointwise...

Wavelet transforms and symmetric tube domains.

Liu, Heping (1998)

Journal of Lie Theory

Weak Containment and Tensor Products of Group Representations.

Eberhard Kaniuth (1982)

Mathematische Zeitschrift

Weak Containment and Tensor Products of Group Representations. II.

Eberhard Kaniuth (1985)

Mathematische Annalen

When is there a discontinuous homomorphism from L¹(G)?

Volker Runde (1994)

Studia Mathematica

Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.