Spherical functions and uniformly bounded representations of free groups

Tadeusz Pytlik

Displaying similar documents to “Spherical functions and uniformly bounded representations of free groups”

An analytic series of irreducible representations of the free group

Ryszard Szwarc (1988)

Annales de l'institut Fourier

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Let $F_{k}$ be a free group on $k$ generators. We construct the series of uniformly bounded representations $\prod_{z}$ of $F_{k}$ acting on the common Hilbert space, depending analytically on the complex parameter z, $1 / (2 k - 1) < | z | < 1$ , such that each representation $\prod_{z}$ is irreducible. If $z$ is real or $| z | = 1 / (\sqrt{2 k - 1})$ then $\prod_{z}$ is unitary; in other cases $\prod_{z}$ cannot be made unitary. For $z \neq z^{'}$ representations $\prod_{z}$ and $\prod_{z^{'}}$ are congruent modulo compact operators.

On a maximum principle in potential theory

Dagmar Medková (1982)

Časopis pro pěstování matematiky

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Volume ratios in $L_{p}$ -spaces

Yehoram Gordon, Marius Junge (1999)

Studia Mathematica

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There exists an absolute constant $c_{0}$ such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that $i n f_{e l l i p s o i d ε \subset B_{E}} {(v o l (B_{E}) / v o l (ε))}^{1 / n} \leq c_{0} i n f_{z o n o i d Z \subset B_{F}} {(v o l (B_{F}) / v o l (Z))}^{1 / k}$ . The concept of volume ratio with respect to $ℓ_{p}$ -spaces is used to prove the following distance estimate for $2 \leq q \leq p < \infty$ : $s u p_{F \subset ℓ_{p}, d i m F = n} i n f_{G \subset L_{q}, d i m G = n} d (F, G) \sim_{c_{p q}} n^{(q / 2) (1 / q - 1 / p)}$ .