Given a unimodular real spherical space $Z=G/H$ we construct for each boundary degeneration $Z_I=G/H_I$ of $Z$ Bernstein morphism $B_I: L^2(Z_I)_{\rm disc }\to L^2(Z)$. We show that $B:=\bigoplus_I B_I$ provides an isospectral $G$-equivariant onto $L^2(Z)$. Further, the maps $B_I$ are finite linear combinations orthogonal projections which translates in known cases where is group or symmetric i...

The problem of representation and analysis of functions defined on manifolds (signals, images, and data in general) is ubiquities in many fields ranging from statistics and cosmology to neuroscience and biology. It is very common to consider input signals as points in a high-dimensional measurement space, however, meaningful structures lay on a manifold embedded in this space. In the last decad...

In this paper, we study the asymptotic behavior of traces Hecke operators for spherical discrete automorphic representations fixed level on general split reductive groups over \(\mathbb {Q}\). Under a condition analytic intertwining operators, which is known classical and exceptional group \(G_2\), obtain expected asymptotics in terms Plancherel measure an explicit estimate remainder.

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.

Strong asymptotic results for relativistic Hermite polynomials H n (z) are established as n, N →∞, thereby supplementing recent results on weak asymptotics for these polynomials. Depending on growth properties of the ratio N/n for the rescaled polynomials H n (cnz) (cn being suitable positive numbers, n, N →∞), formulae of Plancherel-Rotach type are derived on the oscillatory interval, in the c...

Small perturbations of the Jacobi matrix with weights √ n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh formula for the Schrödinger operator on the half-line with summable potential. Additionally a base of generalized eigenvectors for ”free” Hermite ope...