A family of Gaussian analytic functions (GAFs) has recently been linked to the Gabor transform white noises [4]. This answered pioneering work by Flandrin [10], who observed that zeros noise had a regular distribution and proposed filtering algorithms based on spectrogram. In this paper, we study in systematic way link between GAFs class time-frequency transforms noises. Our main observation is...

In [1] we defined symmetry classes, commutation symmetries and symmetry operators in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigated them by means of tools from the representation theory of symmetric groups SN such as decompositions of ideals of the group ring C[SN ], idempotents of C[SN ], discrete Fourier transforms of SN , Littlewood-Richardson p...

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention...

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts. We show here that the same is true in any Rn —the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new...

In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on the theory of representations of generators and relations. By this we mean a finite system of generators which are represented by operators in Hilbert space....

A novel reconstruction method of nanometer micro-displacement Fabry–Perot (F-P) interference is proposed in this study. Hilbert transforms are performed for F-P fringes, and the obtained signal performs tangent operation with original signal. Finally, validity algorithm structure verified by simulation several experimental measurements vibration. Results from experiments show that maximum relat...

In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on the theory of representations of generators and relations. By this we mean a finite system of generators which are represented by operators in Hilbert space....

Simulation of beam cooling usually requires performing certain integral transformations every time step or so, which is a significant burden on the CPU. Examples are the dispersion integrals (Hilbert transforms) in the stochastic cooling, wake fields and IBS integrals. An original method is suggested for fast and sufficiently accurate computation of the integrals. This method is applied for the...

Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the dual group Ẑ = T, and which is recurrent. We also show that there is a Polish monothetic group which is re...