We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel–type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z+ of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z+ which is expressed throug...

In the present paper we construct and solve a differential model for the q-analog of the Plancherel growth process. The construction is based on a deformation of the Makrov-Krein correspondence between continual diagrams and probability distributions.

[2] Apparently Fourier did not possess the inner-product expression for (concrete) Fourier coefficients when he first proposed that functions are expressible in Fourier series. This understandably weakened his claim. Worse, at the time, notions of convergence and even the notion of function were amorphous, so that the sense(s) in which a function might be represented by a Fourier series could n...

This paper uses some basic concepts and results on harmonic analysis associated with Heckman-Opdam theory \(\mathbb {R}^{d}\) to study types of wavelet packets the corresponding transforms. More precisely, we two transforms related hypergeometric Fourier transform W-invariant functions, prove Plancherel, Calderón, reconstruction formulae for these

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel–type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z+ of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z+ which is expressed throug...

We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion‎. ‎In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

Abstract We provide a Plancherel decomposition for the space of symplectic bilinear forms rank $2n$ over local non-Archimedean field $F$ in terms that $\operatorname{GL}_n(F)$.