Concentration estimates for band-limited spherical harmonics expansions via the large sieve principle

We study a concentration problem on the unit sphere $\mathbb{S}^2$ for band-limited spherical harmonics expansions using large sieve methods. We derive upper bounds for concentration in terms of the maximum Nyquist density. Our proof uses estimates of the spherical harmonics coefficients of certain zonal filters. We also demonstrate an analogue of the classical large sieve inequality for spherical harmonics expansions

Unique characterization of the Fourier transform in the framework of representation theory

In this paper we elaborate upon the investigation initiated in [3] of typical and distinctive properties of the Fourier transform (FT), in particular the crucial role played by the Howe dual pair (O(m), sl(2)). We prove in detail a result on the unique characterization of the FT making extensive use of a representation of the Lie algebra sl(2). As an example, we consider the case m = 1. We refer to [3] for a detailed study involving the derivation of a class of operators portraying FT symmetry properties

Bargmann’s versus for fractional Fourier transforms and application to the quaternionic fractional Hankel transform

We present a general formalism `a la Bargmann for constructing fractional Fourier transform associated to specific class of integral transforms on separable Hilbert spaces. As concrete application, we consider the quaternionic fractional Fourier transform on the real half-line and associated to the hyperholomorphic second Bargmann transform for the slice Bergman space of second kind. This leads to an extended version of the well-known fractional Hankel transform. Basic properties are derived including inversion formula and Plancherel identity.Emerging Sources Citation Index (ESCI)MathScinetScopu