Restriction of Fourier transforms to some complex curves

Details Restriction of Fourier transforms to some complex curves Restriction of Fourier transforms to some complex curves

2011-11-28

arxiv.org/abs/1111.6409v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The purpose of this paper is to prove a Fourier restriction estimate for certain 2-dimensional surfaces in $\bbR^{2d}$, $d\ge 3$. These surfaces are defined by a complex curve $\gamma(z)$ of simple type, which is given by a mapping of the form % \[ z\mapsto \gamma (z) = \big(z, \, z^2,..., \, z^{d-1}, \, \phi(z) \big) \] % where $\phi(z)$ is an analytic function on a domain $\Omega \subset \bbC$. This is regarded as a real mapping $z=(x,y) \mapsto \gamma(x,y)$ from $\Omega \subset \bbR^2$ to $\bbR^{2d}$. Our results cover the case $\phi(z) = z^N$ for any nonnegative integer $N$, in all dimensions $d\ge 3$. Furthermore, when $d=3$, we have a uniform estimate, where $\phi(z)$ may be taken to be an arbitrary polynomial of degree at most $N$. These results are analogues of the uniform restricted strong type estimate in \cite{BOS3}, valid for polynomial curves of simple type and some other classes of curves in $\bbR^d$, $d\ge 3$.

Affiliated with

Also associated with

No associations

Rating

Restriction of Fourier transforms to some complex curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Restriction of Fourier transforms to some complex curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Restriction of Fourier transforms to some complex curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-67386