We introduce $\Psi \mathrm{ec}$, a discretization of Cartan's exterior calculus differential forms using wavelets. Our construction consists $r$-form wavelets with flexible directional localization that provide tight frames for the spaces $\Omega^r(\mathbb{R}^n)$ in $\mathbb{R}^2$ and $\mathbb{R}^3$. By construction, satisfy de Rahm co-chain complex, Hodge decomposition, $k$-dimensional integra...

Let Mn stand for the Plancherel measure on Yn, the set of Young diagrams with n boxes. A recent result of R. P. Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with respect to Mn depends on n polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel me...

For a real or p-adic connected reductive group G, Harish-Chandra introduced the Plancherel measure on the tempered dual Ĝtemp and founded the Plancherel formula [7, 18] relating functions on G to functions on Ĝtemp. While the Plancherel measure is equal to the formal degree for square-integrable representations, there has been no similar interpretation for tempered but nonsquare-integrable repr...

So there 5 partitions for 4. Assign each partition with a probability, we then get a probability measure on them. Different ways of assigning probabilities: Uniform measure Plancherel measure Jack measure Restricted uniform measure Restricted Jack measure. We will study the properties of r.v.’s .k1; k2; : : :/, a random partition of n. Example 2. As n!1, under the Plancherel measure, k1 2 p n n...

Résumé Nous prouvons la formule de Plancherel pour les fonctions de Whittaker sur un groupe réductif p-adique. Les méthodes sont proches de celles de la preuve de Waldspurger, d’après Harish-Chandra, pour les fonctions lisses sur le groupe. Au delà du résultat, ce travail met en place un cadre qui devrait s’avérer utile pour d’autres formules de Plancherel, notamment pour les espaces symétrique...

Let F be a nonarchimedean local field, let GL(n) = GL(n, F ) and let ν denote Plancherel measure for GL(n). Let Ω be a component in the Bernstein variety Ω(GL(n)). Then Ω yields its fundamental invariants: the cardinality q of the residue field of F , the sizes m1, . . . ,mt, exponents e1, . . . , et, torsion numbers r1, . . . , rt, formal degrees d1, . . . , dt and the Artin conductors f11, . ...

Let X = G/K be a Riemannian symmetric space of the noncompact type, Γ ⊂ G a discrete, torsion-free, cocompact subgroup, and let Y = Γ\X be the corresponding locally symmetric space. In this paper we explain how the Harish-Chandra Plancherel Theorem for L(G) and results on (g,K)-cohomology can be used in order to compute the L-Betti numbers, the Novikov-Shubin invariants, and the L-torsion of Y ...

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an L2-function on an appropriately chosen group while the Wigner function is defined on a coadjoint orbit of the group and serves ...

Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem...