Abstract. We prove Poincaré and Plancherel–Polya inequalities for weighted p-spaces on weighted graphs in which the constants are explicitly expressed in terms of some geometric characteristics of a graph. We use a Poincaré-type inequality to obtain some new relations between geometric and spectral properties of the combinatorial Laplace operator. Several well-known graphs are considered to dem...

Relative dimensions of isotypic components of N–th order tensor representations of the symmetric group on n letters give a Plancherel– type measure on the space of Young diagrams with n cells and at most N rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant w...

We introduce an integral transform on the space of hyperplanes applying Plancherel formula Radon to definition semiclassical Bargmann Euclidean space. This is similar and some basic facts microlocal analysis are also discussed.

In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part, attention is focussed on the simply connected nilpotent Heisenberg group H. We derive criteria for the existence of discretisations and sampling expansions ...

The description of characters of the innnite symmetric group S1 = lim ?! Sn is considered in the paper as an asymptotical combinatorial problem. It is equivalent to the characterization problem of totally positive sequences. We derive the list of characters, rst obtained by E. Thoma in 1964, using appropriate exact formulae for the number of skew Young tableaux. The character space is treated a...

We study random partitions λ = (λ1, λ2, . . . , λd) of n whose length is not bigger than a fixed number d. Suppose a random partition λ is distributed according to the Jack measure, which is a deformation of the Plancherel measure with a positive parameter α > 0. We prove that for all α > 0, in the limit as n → ∞, the joint distribution of scaled λ1, . . . , λd converges to the joint distributi...

The Diestel-Leader graph DL(q, r) is the horocyclic product of the homogeneous trees with respective degrees q+1 and r+1. When q = r, it is the Cayley graph of the lamplighter group (wreath product) Zq≀Z with respect to a natural generating set. For the “Simple random walk” (SRW) operator on the latter group, Grigorchuk and Żuk and Dicks and Schick have determined the spectrum and the (on-diago...

The problem of finding the explicit Plancherel formulas for semisimple Lie groups has been solved completely in the case of complex semisimple Lie groups (see [3 (b)]). Moreover Harish-Chandra showed [3(f)] that the problem is solved also for a real semisimple Lie group having only one conjugate class of Cartan subgroups. In the case of real semisimple Lie groups with several conjugate classes ...