[e7e09] %Read% #Online~ Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (Am-194) - Isroil A Ikromov ~e.P.u.b~
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Harmonic analysis, the stein restriction problem for a smooth hypersurface s ⊂ rn, asks for of f, and ̂fs denotes the fourier restriction of f to s, where.
The problem of l q ( ℝ 3) → l 2 ( s) fourier restriction estimates for smooth hypersurfaces s of finite type in ℝ 3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up the study of more general l q ( ℝ 3) → l r ( s) fourier restriction estimates, by studying a prototypical model class of two-dimensional surfaces for which the gaussian curvature degenerates in one-dimensional subsets.
Fourier restriction for hypersurfaces in three dimensions and newton polyhedra by isroil a ikromov and detlef müller.
We prove a bilinear restriction theorem for a surface of negative curvature. As a consequence we obtain an almost sharp linear restriction theorem.
We consider the question in which sense the fourier transform may be restricted to smooth.
Feb 1, 2021 this is the statement of the so-called tomas-stein theorem.
In their work ikromov and müller (fourier restriction for hypersurfaces in three dimensions and newton polyhedra. Princeton university press, princeton, 2016) proved the full range \(l^p-l^2\) fourier restriction estimates for a very general class of hypersurfaces in \(\mathbb r^3\) which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed norm case where the coordinates are split in two directions, one tangential and the other.
Aug 5, 2019 abstract in contrast to elliptic surfaces, the fourier restriction problem for hypersurfaces of non‐vanishing gaussian curvature which admit.
To write a preliminary answer as expanded comment, to explain why the tentative answer has a certain problem, although it does make progress: first, a simpler.
The problem of restriction of fourier transform is about estimates for integrals of the form.
Restriction estimates for measures on hypersurfaces have long been a central topic fourier analysis, hausdorff dimension, restriction estimates, maximal oper-.
Other investigators: researcher co-investigators: project partners.
Author (s) this is the first book to present a complete characterization of stein-tomas type fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of lebesgue spaces for which these estimates are valid is described in terms of newton polyhedra associated to the given surface.
As a permanent source of inspiration in the preparation of this talk i would like to single out stein’s book [47]. For further reading about related topics i recommend the books [36,37,42,48] and the article [49] dealing with several.
This is the first book to present a complete characterization of stein-tomas type fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of lebesgue spaces for which these estimates are valid is described in terms of newton polyhedra associated to the given surface.
Let ̂s be a smooth compact hypersurface in ̂r n with non vanishing.
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Abstract: conditional on fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we obtain uniform--depending only on the dimension and polynomial degree--estimates for restriction with affine surface measure, slightly beyond the bilinear range.
Christ, on the restriction of the fourier transform to curves: endpoint results and degenerate cases, trans.
5) this generalizes bilinear restriction estimates for hypersurfaces with nonvanishing gaussian curvature [10,20,22,24,25]. The sharp bilinear restrict estimates were first proven by tao [20] for elliptic surfaces and later these was extended to more general surfaces by the author [10] and vargas [25].
Fourier restriction for hypersurfaces in three dimensions and newton polyhedra (am-194) book description: this is the first book to present a complete characterization of stein-tomas type fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.
An affine fourier restriction theorem for conical surfaces - volume 60 issue 2 skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites.
Scale invariant fourier restriction to a hyperbolic surface preprint version. Coordinates adapted to vector fields i: canonical coordinates arxiv version. Linear and bilinear restriction to certain rotationally symmetric hypersurfaces.
L p-l 2 f ourier restriction theore m for a large class of smoo th, finite type hype rsurfaces in r 3 which includes in pa rticular all rea l-analytic hypersurfaces.
Oct 30, 2017 updated description:members of the community were invited to attend a public lecture that explored the deep connection between elementary.
In paragraph 3 we state the results that we have obtained for hypersurfaces σ given as the graph of certain homogeneous polynomial functions.
We will extend the fourier restriction inequality for quadratic hypersurfaces obtained by strichartz. We will consider the case where the hypersurface is a graph of a certain real polynomial which is a sum of one-dimensional monomials. It is essential to examine the decay of a one-dimensional oscillatory integral.
We consider a surface with negative curvature in $\bbb r^3$ which is a cubic perturbation of the saddle.
Lee fourier restriction for hypersurfaces in three dimensions and newton polyhedra (am-194) por detlef müller disponible en rakuten kobo. This is the first book to present a complete characterization of stein-tomas type fourier restriction estimates for larg.
S/ fourier restriction estimates for smooth hypersurfaces s of finite type hypersurfaces with k ─ n2 nonvanishing principal curvatures [lee and vargas 2010].
In contrast to elliptic surfaces, the fourier restriction problem for hypersurfaces of non-vanishing gaussian curvature which admit principal curvatures of opposite signs is still hardly understood.
Sep 1, 2008 a necessary condition is established for the optimal (lp,l2) restriction theorem to hold on a hypersurface s, in terms of its gaussian curvature.
We will extend the fourier restriction inequality for quadratic hypersurfaces obtained by strichartz. We will consider the case where the hypersurface is a graph of a certain real polynomial which is a sum of one-dimensional monomials. It is essential to examine the decay of a one-dimensional oscillatory.
Fourier restriction for hypersurfaces in three dimensions and this is the first book to present a complete characterization of stein-tomas type fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.
May 30, 2018 the fourier restriction problem is the following general question. Suppose one has a smooth compact hypersurface s in r d then the surface.
A fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $l^p - l^q $ restriction theorem for compact subsets of a type $k$ conical surface, up to an endpoint. Furthermore, the chosen weight is shown to be, in some quantitative sense, optimal.
Zhou in which we use min-max techniques to prove existence of closed hypersurfaces with prescribed.
Hypersurfaces share, with surfaces in a three-dimensional space, the property of being defined by a single implicit equation, at least locally (near every point), and sometimes globally. A hypersurface in a (euclidean, affine, or projective) space of dimension two is a plane curve.
4:00pm – 4:50pm edt, conference plenary talk ii: betsy stovall (university of wisconsin-madison), “fourier restriction to degenerate hypersurfaces”.
The problem of $l^p (r^3)\to l^2 (s)$ fourier restriction estimates for smooth hypersurfaces s of finite type in r^3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up the study of more general $l^p (r^3)\to l^q (s)$ fourier restriction estimates, by studying a prototypical class of two-dimensional surfaces with strongly varying curvature conditions.
Pdf in their work ikromov and müller (fourier restriction for hypersurfaces in three dimensions and newton polyhedra.
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