Download e-book for iPad: Fourier Restriction for Hypersurfaces in Three Dimensions by Isroil A. Ikromov,Detlef Müller

This is the 1st booklet to provide an entire characterization of Stein-Tomas sort Fourier restrict estimates for big periods of delicate hypersurfaces in 3 dimensions, together with all real-analytic hypersurfaces. the diversity of Lebesgue areas for which those estimates are legitimate is defined by way of Newton polyhedra linked to the given surface.

Isroil Ikromov and Detlef Müller commence with Elias M. Stein's inspiration of Fourier limit and a few family among the decay of the Fourier remodel of the skin degree and Stein-Tomas variety limit estimates. Varchenko's principles touching on Fourier decay to linked Newton polyhedra are in brief defined, really the concept that of tailored coordinates and the idea of top. It seems that those classical instruments basically suffice already to regard the case the place there exist linear tailored coordinates, and hence Ikromov and Müller be aware of the remainder case. the following the idea of r-height is brought, which proves to be the fitting new thought. They then describe decomposition innovations and similar preventing time algorithms that permit to partition the given floor into numerous items, that may finally be dealt with through oscillatory essential estimates. varied interpolation innovations are offered and used, from advanced to more moderen genuine equipment through Bak and Seeger.

Fourier restrict performs a major position in different fields, specifically in actual and harmonic research, quantity idea, and PDEs. This ebook will curiosity graduate scholars and researchers operating in such fields.