Related papers: A Note on the Convolution of Circle Impulses
We prove an asymptotic formula for the second moment of $L$-functions associated to the Rankin-Selberg convolution of two holomorphic Hecke cusp forms with equal weight.
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products on the space of Chinese characters. The…
We calculate production cross sections of a single rotating string from a collision of two light states in bosonic string theory. We find that the cross sections are written in terms of the modified Bessel function of the first kind with…
We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated…
A comprehensive analysis of the elementary processes behind the scanning tunneling microscope controlled rotation of C$_2$H$_2$ and C$_2$D$_2$, isotopologues of a single acetylene molecule adsorbed on the Cu(001) surface is given, with a…
We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. More generally, we develop formulae for integrals of…
The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion.…
We provide a formula to compute the volume of the intersection of a generalized cylinder with a hyperplane. Then we prove an integral inequality involving Bessel functions similar to Keith Ball's well-known inequality. Using this inequality…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give…
We consider the convolution equation $(\delta - J) * G = g$ on $\mathbb R^d$, $d>2$, where $\delta$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as…
The semi-discrete convolution with the Box Spline is an important tool in approximation theory. We give a formula for the difference between semi-discrete convolution and convolution with the Box Spline. This formula involves multiple…
We consider particle trajectories in the gravitational field of an impulsive pp-wave. Due to the distributional character of the wave profile one inevitably encounters an ambiguous point value $\theta(0)$. We show that this ambiguity may be…
A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate…
There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.