Oscillatory integral operators with homogeneous polynomial phases in several variables

Details Oscillatory integral operators with homogeneous polynomial phases in several variables Oscillatory integral operators with homogeneous polynomial phases in several variables

2006-05-03

arxiv.org/abs/math/0605102v2

Mathematics

Classical Analysis and ODEs

39 pages, 2 figures; minor corrections; to appear in Journal of Functional Analysis

Scientific paper

We obtain $L^2$ decay estimates in $\lambda$ for oscillatory integral operators whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of (2+2)--dimensions for any m while, in higher dimensions, the result is sharp for m sufficiently large. The proof for large $m$ follows from essentially algebraic considerations. For cubics in (2+2)--dimensions, the proof involves decomposing the operator near the conic zero variety of the determinant of the Hessian of the phase function, using an elaboration of the general approach of Phong and Stein [1994].

Affiliated with

Also associated with

No associations

Rating

Oscillatory integral operators with homogeneous polynomial phases in several variables 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 Oscillatory integral operators with homogeneous polynomial phases in several variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Oscillatory integral operators with homogeneous polynomial phases in several variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-307490