Matrix elements of Fourier Integral Operator

2014 ◽  
pp. 281-309
Author(s):  
Steve Zelditch
Keyword(s):  
Integral Operator ◽  
Fourier Integral Operator ◽  
Fourier Integral ◽  
Matrix Elements

scholarly journals The weak-type (1,1) of Fourier integral operators of order –(n–1)/2

2004 ◽  
Vol 76 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Terence Tao
Keyword(s):  
Hardy Space ◽  
Integral Operator ◽  
Weak Type ◽  
Fourier Integral Operator ◽  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Main Ideas

AbstractLet T be a Fourier integral operator on Rn of order–(n–1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.

scholarly journals Higher Order Scattering on Asymptotically Euclidean Manifolds

2000 ◽  
Vol 52 (5) ◽  
pp. 897-919
Author(s):  
T. J. Christiansen ◽  
M. S. Joshi
Keyword(s):  
Integral Operator ◽  
Finite Number ◽  
Geodesic Flow ◽  
Scattering Theory ◽  
Short Range ◽  
Fourier Integral Operator ◽  
Fourier Integral ◽  
Scattering Matrix ◽  
Higher Order ◽  
The Absolute

AbstractWe develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time π on the boundary. Furthermore, it is shown that on n the asymptotics of certain short-range perturbations of Δk can be recovered from the scattering matrix at a finite number of energies.

scholarly journals Local Formula for the Index of a Fourier Integral Operator

2001 ◽  
Vol 59 (2) ◽  
pp. 269-300 ◽  
Author(s):  
Eric Leichtnam ◽  
Ryszard Nest ◽  
Boris Tsygan
Keyword(s):  
Integral Operator ◽  
Fourier Integral Operator ◽  
Fourier Integral

ON THE BEHAVIOR AT INFINITY OF THE FUNDAMENTAL SOLUTION OF TIME DEPENDENT SCHRÖDINGER EQUATION

2001 ◽  
Vol 13 (07) ◽  
pp. 891-920 ◽  
Author(s):  
KENJI YAJIMA
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operator ◽  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Fourier Integral Operator ◽  
Fourier Integral ◽  
Time Dependent ◽  
Initial Value

We show that the asymptotic behavior at infinity of the fundamental solution of the initial value problem for the free Schrödinger equation or of the harmonic oscillator at non-resonant time is stable under subquadratic perturbations. We also show that the same is true for the phase and the amplitude of the Fourier integral operator representing the propagator.

Sign in / Sign up

Export Citation Format

Share Document