The Fourier extension operator on large spheres and related oscillatory integrals
نویسندگان
چکیده
منابع مشابه
The Fourier Extension Operator on Large Spheres and Related Oscillatory Integrals
We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...
متن کامل2 1 Se p 20 06 THE FOURIER EXTENSION OPERATOR ON LARGE SPHERES AND RELATED OSCILLATORY
We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L p (S 2) → L q (RS 2) estimates for the Fourier extension operator on large spheres in R 3 , which are uniform in the ra...
متن کامل. C A ] 4 A ug 2 00 6 THE FOURIER EXTENSION OPERATOR ON LARGE SPHERES AND RELATED OSCILLATORY
We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...
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We introduce and analyse the so-called Fourier extension method for the approximation of oscillatory phenomena in bounded intervals. As we show, this method possesses good resolution properties for such problems. In particular, the resolution constant, the number of degrees of freedom per wavelength required to resolve an oscillation at a given frequency, can be varied between 2 and π by a user...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2008
ISSN: 0024-6115
DOI: 10.1112/plms/pdn022