Zobrazeno 1 - 10
of 128
pro vyhledávání: '"de la Harpe, Pierre"'
Autor:
de la Harpe, Pierre
It is shown that there are groups $\Gamma$ with finite generating sets $S$ such that the adjacency operator of the Cayley graph ${\rm Cay}(\Gamma,S)$ is a disjoint union of $N$ intervals, for arbitrarily large integers $N$.
Externí odkaz:
http://arxiv.org/abs/2402.06279
Autor:
de la Harpe, Pierre
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this article is to
Externí odkaz:
http://arxiv.org/abs/2308.04339
Autor:
de la Harpe, Pierre
Let $X$ be a closed smooth manifold, $G$ be a simple connected compact real Lie group, $M (G)$ be the group of all smooth maps from $X$ to $G$, and $M_0 (G)$ be its connected component for the $\mathcal C^\infty$-compact open topology. It is shown th
Externí odkaz:
http://arxiv.org/abs/2301.03494
A graph $G = (V, E)$ of bounded degree has an adjacency operator~$A$ which acts on the Hilbert space $\ell^2(V)$. There are different kinds of measures of interest on the spectrum $\Sigma (A)$ of $A$. In particular, each vector $\xi \in \ell^2(V)$ de
Externí odkaz:
http://arxiv.org/abs/2205.12819
Autor:
de la Harpe, Pierre
The subject of growth of groups has been active in the former Soviet Union since the early 50's and in the West since 1968, when articles of \v{S}varc and Milnor have been published, independently. The purpose of this note is to quote a few articles
Externí odkaz:
http://arxiv.org/abs/2106.02499
Autor:
Bekka, Bachir, de la Harpe, Pierre
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a special att
Externí odkaz:
http://arxiv.org/abs/1912.07262
Let $G$ be a group. A subset $F \subset G$ is called irreducibly faithful if there exists an irreducible unitary representation $\pi$ of $G$ such that $\pi(x) \neq \mathrm{id}$ for all $x \in F \smallsetminus \{e\}$. Otherwise $F$ is called irreducib
Externí odkaz:
http://arxiv.org/abs/1807.04992
Autor:
de la Harpe, Pierre
For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of degree (Br
Externí odkaz:
http://arxiv.org/abs/1609.06637
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book arXiv:1403.3796<
Externí odkaz:
http://arxiv.org/abs/1606.05539
Autor:
Bacher, Roland, De La Harpe, Pierre
It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed, for other g
Externí odkaz:
http://arxiv.org/abs/1603.07943