The measure algebras of the title are those which are also hypergroups with some regularity conditions, Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series, It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions, The...

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in statistical physics of growing/melting crystals, T.A.S.E.P., and also in algebraic geometry. In particular we compute the Gromov-Witten invariants of the Xp = O(p...

Let V be a finite dimensional real vector space. Let V alsm(V ) be the space of translation invariant smooth valuations on convex compact subsets of V . Let Dens(V ) be the space of Lebesgue measures on V . The goal of the article is to construct and study an isomorphism FV : V alsm(V )−̃→V alsm(V ∗)⊗Dens(V ) such that FV commutes with the natural action of the full linear group on both spaces, ...

(3) v = fdju + vc for the decomposition into discrete (ƒ dju as above) and continuous vc parts. Let F = û = J2k' + J'e' dvc{y) be the Fourier transform of the measure v. Then Wiener's theorem says (2) continues to hold. This means that the Fourier transform vc of the continuous portion of the measure does not contribute to the Bohr mean of |F|. We will interpret Wiener's theorem to mean that ev...

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ iΩ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of GL(Ω). Using Riesz distributions, an explicit int...

We recall the notion of cuspform for Γ = SL2(Z) acting on the upper half-plane, and prove that the orthogonal complement in L(Γ\H) to cuspforms is spanned by pseudo-Eisenstein series, which in turn are expressible as wave packets of Eisenstein series Es. Further we have a Plancherel theorem for this space. The non-trivial harmonic analysis resides in the application of the Fourier transform on ...

A recent addition to the class of integral transforms is quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this insufficient for addressing spectrum non-stationary signals in domain. To address problem, we, paper, study (two sided) windowed (QWQPFT) investigate uncertainty principles associated with QWQPFT. We first prop...

This paper contains two results concerning the spectral decomposition, in a broad sense, of space nondegenerate Hermitian matrices over local field characteristic zero. The first is an explicit Plancherel decomposition associated L2 thus confirming conjecture Sakellaridis-Venkatesh this particular case. second formula for multiplicities generic representations p-adic case that extends previous ...