scholarly journals Bilinear Fourier Restriction Theorems

2012 ◽  
Vol 18 (6) ◽  
pp. 1265-1290
Author(s):  
Ciprian Demeter ◽  
S. Zubin Gautam
Keyword(s):  
Fourier Restriction ◽  
Restriction Theorems

Fourier restriction theorems for curves with affine and Euclidean arclengths

1985 ◽  
Vol 97 (1) ◽  
pp. 111-125 ◽  
Author(s):  
S. W. Drury ◽  
B. P. Marshall
Keyword(s):  
Fourier Transform ◽  
Smooth Manifold ◽  
Fourier Restriction ◽  
Survey Article ◽  
Restriction Theorems ◽  
Schwartz Class ◽  
The Fourier Transform ◽  
Image Position

Let M be a smooth manifold in . One may ask whether , the restriction of the Fourier transform of f to M makes sense for every f in . Since, for does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequalityfor every f in (say) the Schwartz class. Results of this kind are called restriction theorems. An excellent survey article on this subject is to be found in Tomas[13].

Fourier restriction theorems for degenerate curves

1987 ◽  
Vol 101 (3) ◽  
pp. 541-553 ◽  
Author(s):  
S. W. Drury ◽  
B. P. Marshall
Keyword(s):  
Finite Order ◽  
Smooth Manifold ◽  
Fourier Restriction ◽  
Restriction Theorems ◽  
Image Position

Fourier restriction theorems contain estimates of the formwhere σ is a measure on a smooth manifold M in ∝n. This paper is a continuation of [5], which considered this problem for certain degenerate curves in ∝n. Here estimates are obtained for all curves with degeneracies of finite order. References to previous work on this problem may be found in [5].

RESTRICTION THEOREMS IN REAL ANALYSIS

1994 ◽  
Vol 20 (2) ◽  
pp. 510 ◽  
Author(s):  
Brown
Keyword(s):  
Real Analysis ◽  
Restriction Theorems

RESTRICTION THEOREMS IN REAL ANALYSIS

1994 ◽  
Vol 20 (2) ◽  
pp. 411
Author(s):  
Brown
Keyword(s):  
Real Analysis ◽  
Restriction Theorems

Quantum Ergodic Restriction Theorems: Manifolds Without Boundary

2013 ◽  
Vol 23 (2) ◽  
pp. 715-775 ◽  
Author(s):  
John A. Toth ◽  
Steve Zelditch
Keyword(s):  
Restriction Theorems

scholarly journals Time-Harmonic Solutions for Maxwell’s Equations in Anisotropic Media and Bochner–Riesz Estimates with Negative Index for Non-elliptic Surfaces

2021 ◽  
Author(s):  
Rainer Mandel ◽  
Robert Schippa
Keyword(s):  
Gaussian Curvature ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Smooth Surfaces ◽  
Negative Index ◽  
Elliptic Surfaces ◽  
Conical Singularities ◽  
Fourier Restriction ◽  
Time Harmonic ◽  
Homogeneous Media

AbstractWe solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $$L^p$$ L p -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.

scholarly journals Fourier restriction to polynomial curves I: a geometric inequality

2010 ◽  
Vol 132 (4) ◽  
pp. 1031-1076 ◽  
Author(s):  
Spyridon Dendrinos ◽  
James Wright
Keyword(s):  
Geometric Inequality ◽  
Polynomial Curves ◽  
Fourier Restriction
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