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Valette, Alain
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Valette, Alain
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Professeur ordinaire
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alain.valette@unine.ch
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Voici les éléments 1 - 10 sur 102
- PublicationMétadonnées seulement
- PublicationMétadonnées seulementIsometric group actions on banach spaces and representations vanishing at infinity(2008)
;De Cornulier, Yvan ;Tessera, RomainOur main result is that the simple Lie group G = Sp( n; 1) acts metrically properly isometrically on L-p( G) if p > 4 n + 2. To prove this, we introduce Property (BP0V), with V being a Banach space: a locally compact group G has Property (BP0V) if every affine isometric action of G on V, such that the linear part is a C-0- representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic groups over a local field of characteristic zero, have Property ( BP V 0). As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology with respect to the left regular representation on L-2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L-2- Betti number is nonzero. - PublicationMétadonnées seulementOn the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator(1997)
; ; Zuk, AndrzejHarper's operator is the self-adjoint operator on l(2)(Z) defined by N(theta,phi)xi(n) = xi(n + 1) + xi(n - 1) + 2 cos(2 pi(n theta + phi))xi(n) (xi is an element of l(2)(Z), n is an element of Z, theta, phi is an element of [0, 1]). We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bound on the norm of H-theta,H-phi:\\H-theta,H-phi\\ less than or equal to 2(1 + root 2 + cos(2 pi theta)). We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H-theta,H-phi as the image of H-theta = U-theta + U-theta* + V-theta + V-theta* in a suitable representation of the rotation algebra A(theta). We also use powers of H-theta to obtain various upper and lower bounds on \\H-theta\\ = max(phi) \\H-theta,H-phi\\. We show that ''Fourier coefficients'' of H-theta(k) in A(theta) have a combinatorial interpretation in terms of paths in the square lattice Z(2). This allows us to give some applications to asymptotics of lattice paths combinatorics. - PublicationMétadonnées seulement
- PublicationMétadonnées seulementThe Euclidean distortion of the lamplighter group(2010)
;Austin, Tim ;Naor, Assaf - PublicationMétadonnées seulement