The main objective of this paper is to study the composition continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet (WPT) based on (KL-transform). Estimates for KL-wavelet are obtained, Plancherel?s relation WPT-transform derived. Reconstruction formula WPT associated KL-transform also deduced at end Calderon?s related using its convolution property obtained.

Abstract We show that an orthogonal root number of a tempered L -parameter $$\varphi $$ φ decomposes as the product two other numbers: principal parameter and value on central involution Langlands’s character for . The formula resolves conjecture Gross Reeder computes numbers Weil–Deligne representations aris...

We derive a general expression for the Hankel determinants of a Dirichlet series F (s) and derive the asymptotic behavior for the special case that F (s) is the Riemann zeta function. In this case the Hankel determinant is a discrete analogue of the Selberg integral and can be viewed as a matrix integral with discrete measure. We brie y comment on its relation to Plancherel measures.

In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, which call Siegel manifolds. These are entire functions exponential type whose restrictions to given submanifold \(L^p\)-integrable with respect natural measure. For these spaces, among other results, prove the Plancherel–Pólya inequality, inequality sufficient condition for sequence be sampling.

In this paper, we obtain a complete list of inequivalent irreducible representations the compact quantum group [Formula: see text] for nonzero complex deformation parameters text], which are not roots unity. The matrix coefficients these described in terms little text]-Jacobi polynomials. Haar state is shown to be faithful and an orthonormal basis obtained. Thus, have explicit description Peter...

We propose a nonparametric estimator of the expected discounted penalty function in compound Poisson risk model. use projection on Laguerre basis and we compute coefficients using Plancherel theorem. provide an upper bound MISE our estimator, show it achieves parametric rates convergence Sobolev–Laguerre spaces without needing bias-variance compromise. Moreover, compare with deconvolution metho...