Lechao Xiao

activity

20132026

most citedWide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent

290 citations · 701 across the 29 of their papers we have counts for

collaborators

Showing math.CAShow all

7 papers · 1 filter

math.CA2019

Oscillatory Loomis-Whitney and Projections of Sublevel Sets

Maxim Gilula, Kevin O'Neill, Lechao Xiao

We consider an oscillatory integral operator with Loomis-Whitney multilinear form. The phase is real analytic in a neighborhood of the origin in $R^{d}$ and satisfies a nond…

math.CA2016★ 1 cited

Higher decay inequalities for multilinear oscillatory integrals

Maxim Gilula, Philip T. Gressman, Lechao Xiao

In this paper we establish sharp estimates (up to logarithmic losses) for the multilinear oscillatory integral operator studied by Phong, Stein, and Sturm and Carbery and Wright on…

math.CA2016

Endpoint estimates for one-dimensional oscillatory integral operator

Lechao Xiao

The one-dimensional oscillatory integral operator associated to a real analytic phase $S$ is given by $T_{λ} f (x) = \int_{- \infty}^{\infty} e^{iλ S (x, y)} χ (x, y) f (y) d y .$ In this pape…

math.CA2015★ 1 cited

Maximal Decay Inequalities for Trilinear oscillatory integrals of convolution type

Philip T. Gressman, Lechao Xiao

In this paper we prove sharp $L^{\infty}$ - $L^{\infty}$ - $L^{\infty}$ decay for certain trilinear oscillatory integral forms of convolution type on $R^{2}$ . These estimates imply ear…

math.CA2014★ 1 cited

Bilinear Hilbert transforms associated to plane curves

Jingwei Guo, Lechao Xiao

We prove that the bilinear Hilbert transforms and maximal functions along certain general plane curves are bounded from $L^{2} (R) \times L^{2} (R)$ to $L^{1} (R)$ …

math.CA2013★ 4 cited

Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities

Lechao Xiao

We obtain sharp estimates for certain trilinear oscillatory integrals. In particular, we extend Phong and Stein's seminal result to a trilinear setting. This result partially answe…

math.CA2013★ 5 cited

Uniform estimates for bilinear Hilbert transform and bilinear maximal functions associated to polynomials

Xiaochun Li, Lechao Xiao

We study the bilinear Hilbert transform and bilinear maximal functions associated to polynomial curves and obtain uniform $L^{r}$ estimates for $r > \frac{d - 1}{d}$ and this index is sh…