Discrete fractional Radon transforms and quadratic forms

Details Discrete fractional Radon transforms and quadratic forms Discrete fractional Radon transforms and quadratic forms

2010-05-21

arxiv.org/abs/1005.4049v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\ell^p$ to $\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.

Affiliated with

Also associated with

No associations

Rating

Discrete fractional Radon transforms and quadratic forms 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 Discrete fractional Radon transforms and quadratic forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete fractional Radon transforms and quadratic forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-340399