Symmetry problems in harmonic analysis

Harmonic Sliding Analysis Problems

Harmonic sliding analysis (HSA) is a dynamic spectrum analysis [1] in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval. Such a harmonic analysis is necessary for time-frequency localization [2] of analysed signal given peculiarities. Using the well-known Fast Fourier transform (FFT)...

Some Problems in Local Harmonic Analysis

The purpose of this article is to discuss some questions in the harmonic analysis of real and padic groups. We shall be particularly concerned with the properties of a certain family of invariant distributions. These distributions arose naturally in a global context, as the terms on the geometric side of the trace formula. However, they are purely local objects, which include the ordinary invar...

Problems in Harmonic Analysis on Causal Symmetric

Problems in Harmonic Analysis Related To

X \R(1 r\\ f /OO # / ( * ) --> e-*0 \B(e9 X)\ JB(t,x) for certain types of «-dimensional sets B(e9 x) shrinking to x as e -* 0. (\B(e9 x)\ is of course the Lebesgue measure of B(e9 x).) Some standard examples of sets B(e9 x) are balls with center x and radius e, and cubes with center x and diameter e. The problem of considering other sets besides balls and cubes for B(e9 x) received much attent...

Harmonic analysis of equine hoof form and its matched symmetry

This study uses elliptic Fourier analysis (EFA), an outline method of shape analysis, for describing hoof contours symmetries in the Catalan Pyrenean Horse (“Cavall Pirinenc Català”, CPC), a breed from the Spanish Pyrenees. Hoof outlines of 54 limbs (26 forelimbs and 28 hindlimbs, including the same number of left and right limbs) obtained from 15 CPC horses were compared using EFA. Symmetry wa...