Related papers: Decay Rates for Cusp Functions
Assuming that a function and its Fourier transform are dominated by Gaussians, a sharp estimate for the rate of exponential decay of its Hermite coefficients is obtained in terms of the variances of the dominating Gaussians.
The purpose of this paper is to study products of Fourier coefficients of an elliptic cusp form, $a(n)a(n + r)$ $(n \geq 1)$ for a fixed positive integer $r$, concerning both non-vanishing and non-negativity.
We review a variety of topics related to hadronic structure functions in exclusive semihadronic tau decays. We introduce the concept of structure functions and summarize the most important concepts. We then calculate the decay $\tau \to 3…
We discuss rapid decay functions on odometer Cantor spaces and their noncommutative geometry applications.
In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive…
We compute the rate of decay of the persistence probabilities of spherical fractional Brownian motion, which was defined by L\'evy (1965) and Istas (2005). The rate resembles the Euclidean case treated in Molchan (1999). As a by-product we…
We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group $\mathrm{U}(2,n)$. By studying the theta lifts of holomorphic modular forms from $\mathrm{U}(1,1)$, we…
In this article, we establish quantitative results for sign changes in certain subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form of arbitrary degree over congruence subgroups. As a corollary of our result for…
We obtain the decay bounds for Chebyshev series coefficients of functions with finite Vitali variation on the unit square. A generalization of the well known identity, which relates exact and approximated coefficients, obtained using the…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
We address the study of decay rates of solutions to dissipative equations. The characterization of these rates is given for a wide class of linear systems by the {\em decay character}, which is a number associated to the initial datum that…
The cusp effect in K \to 3\pi and data on K_e4 decays allow one to extract experimental information on the elastic \pi\pi scattering amplitude near threshold, and to confront the outcome of the analyses with predictions made in the…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
Let $\G\subset \mathrm{SL}_{2}(\R)$ be a cofinite Fuchsian subgroup, and let $i\infty$ be a cusp of $\G$. For $k\in\Z_{\geq 0}$, let $\Sk$ denote the complex vector space of cusp forms of weight-$k$, with respect to the Fuchsian subgroup…
A relativistic constituent quark model is adopted to give an unified description of the leptonic and semileptonic decays of pseudoscalar mesons (\pi, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to…
The pion mass difference generates a pronounced cusp in the pi0 pi0 invariant mass distribution of K+ --> pi0 pi0 pi+ decays. As originally pointed out by Cabibbo, an accurate measurement of the cusp may allow one to pin down the S-wave…
There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion…
Two aspects of isospin breaking in the decay $K^\pm \to \pi^0 \pi^0 e^\pm \stackrel{_{(-)}}{\nu_e}$ are studied and discussed. The first addresses the possible influence of the phenomenological description of the unitarity cusp on the…