Related papers: Generalized moments of spectral functions from sho…
We study zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We prove that the a limiting horizontal mean counting-measure of the zeroes exists almost surely, and that it is…
Integral expressions for positive-part moments E X_+^p (p>0) of random variables X are presented, in terms of the Fourier-Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events.…
We formulate and derive a generalization of an orthogonal rational-function basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener are a mapping and weighting of the…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
We prove that the $k$-th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x+H]$ matches the corresponding Gaussian moment, as long as $H\ll x/(\log x)^{2k^2+2+o(1)}$ and $H$ tends…
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both…
We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for…
We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete…
We demonstrate a phenomenon of condensation of the Fourier transform $\widehat{f}$ of a function $f$ defined on the real line $\mathbb{R}$ which decreases rapidly on one half of the line. For instance, we prove that if $f$ is…
We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a…
We consider the whole-plane SLE conformal map f from the unit disk to the slit plane, and show that its mixed moments, involving a power p of the derivative modulus |f'| and a power q of the map |f| itself, have closed forms along some…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
It is shown that the method of eliminating the statistical fluctuations from event-by-event analysis proposed recently by Fu and Liu can be rewritten in a compact form involving the generalized factorial moments.
The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…
We prove sharp upper bounds for sums of eigenvalues (and other spectral functionals) of Laplace-like operators, including bi-Laplacian and fractional Laplacian. We show that among linear images of a highly symmetric domain, our spectral…
We elaborate a cut (truncated) Mellin moments (CMM) approach that is constructed to study deep inelastic scattering in lepton-hadron collisions at the natural kinematic constraints. We show that generalized CMM obtained by multiple…