相关论文: On oscillatory integrals with H\"older phases
In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard one-dimensional van der Corput lemma with the…
We derive a general procedure for evaluating the ${\rm n}$th derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded…
Using some resolution of singularities methods of the author, a generalization of a well-known theorem of Varchenko relating decay of oscillatory integrals to the Newton polyhedron is proven. They are derived from analogous results for…
The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary…
We propose homotopy analysis method in combination with Galerkin projections to approximate the natural response of non-smooth oscillators with discontinuities of type Heaviside, signum, modulus etc. While constructing the homotopy, we…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelliptic analogue of the Mumford conjecture (Madsen--Weiss…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the…
We generalize Bourgain's theorem on the decay of the Fourier transform of the multiplicative convolution of measures on $\mathbb R$ to the ring $\mathbb R^n$, where the multiplication is given by coordinate multiplication.
We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…
We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces in terms of estimates in another smaller reference Banach space. This applies to a class of operators…
We explore a signature of phase correlations in Fourier modes of dark matter density fields induced by nonlinear gravitational clustering. We compute the distribution function of the phase sum of the Fourier modes,…
Let X be an arbitrary centered Gaussian process whose trajectories are, with probability one, continuous nowhere differentiable functions. It follows from a classical result, derived from zero-one law, that, with probability one, the…
In this paper we study the local regularity of fractional integrals of Fourier series using several definitions of the H\"older exponent. We especially consider series coming from fractional integrals of modular forms. Our results show that…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.
We consider the question of when it is possible to force a degenerate scalar oscillatory integral to decay as fast as a nondegenerate one by restricting the support to the region where the Hessian determinant of the phase is bounded below.…
Let $f$ be a Rademacher or Steinhaus random multiplicative function. For various arithmetically interesting subsets $\mathcal A\subseteq [1, N]\cap\mathbb N$ such that the distribution of $\sum_{n\in \mathcal A} f(n)$ is approximately…