Related papers: Oscillatory integrals and weighted gradient flows

We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…

In this paper, we furnish van der Corput types estimates for oscillatory integrals with respect to a large parameter, where the phase is allowed to have a stationary point of real order and the amplitude to have an integrable singularity.…

In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…

Filon-Simpson quadrature rules are derived for integrals of the type \int_a^b dx f(x) sin(xy)/(xy) and \int_a^b dx f(x) 4 sin^2(xy/2)/(xy)^2 which are needed in applications of the worldline variational approach to Quantum Field Theory.…

This paper is devoted to $L^2$ estimates for trilinear oscillatory integrals of convolution type on $\mathbb{R}^2$. The phases in the oscillatory factors include smooth functions and polynomials. We shall establish sharp $L^2$ decay…

At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position…

We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate…

We consider the vector functions in a domain homeomorphic to a spherical layer bounded by twice continuously differentiable surfaces. Additional restrictions are imposed on the domain, which allow to conduct proofs using simple methods. On…

We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…

We consider a class of H\"ormander-type oscillatory integral operators in $\mathbb{R}^n$ for $n \geq 3$ odd with real analytic phase. We derive weak conditions on the phase which ensure $L^p$ bounds beyond the universal $p \geq 2 \cdot…

We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…

Using an analogy with the well-known double-slit experiment, we show that the standard phase of neutrino oscillations is correct, refuting recent claims of a factor of two correction. We also improve the wave packet treatment of neutrino…

Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative…

The stability under phase perturbations of the decay rate of local scalar oscillatory integrals in two dimensions is analyzed. For a smooth phase S(x,y) and a smooth perturbation function f(x,y), the decay rate for phase S(x,y) + tf(x,y) is…

Let T be an oscillatory integral operator on L^2(R) with a smooth real phase function S(x,y). We prove that, in all cases but the one described below, after localization to a small neighborhood of the origin the norm of T decays like…

We estimate simple combination of the parabolic cylinder functions and their derivatives. These estimates are important for the spectral analysis of non-analytically perturbed quantum harmonic oscillator. The estimates are valid in rather…

In this paper we develop elements of the global calculus of Fourier integral operators in $R^n$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev $L^2$ estimates for a class of Fourier…

We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…

It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…

We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency $1/\Delta_n$, with $\Delta_n$ going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of…