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A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/7/14
This paper is concerned with the fast computation of Fourier integral operators of the general form Rd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
FAST COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/7/14
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation, general hyperbolic equations, an...
FAST WAVE COMPUTATION VIA FOURIER INTEGRAL OPERATORS
Wave equations Fourier integral operators discrete symbol calculus random sampling separated approximation multiscale computations
2015/7/14
This paper presents a numerical method for “time upscaling” wave equations, i.e., performing time steps not limited by the Courant-FriedrichsLewy (CFL) condition. The proposed method leverages recent ...
A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS
Fourier integral operators the butterfly algorithm hierarchical decomposition separated representation
2015/7/14
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(x,ξ)f (ξ)dξ, where Φ(x, ξ) is a phase funct...
A recent body of work introduced new tight-frames of curvelets [3, 4] to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimall...
Fast Computation of Fourier Integral Operators
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/6/17
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations....
A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
Fourier integral operators the butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/6/17
This paper is concerned with the fast computation of Fourier integral operators of the general form RRd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One
Real-Variable Theory Fourier Integral Operators Semisimple Lie Groups Symmetric Spaces Real Rank One
2014/4/3
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
Approximation of Fourier Integral Operators by Gabor multipliers
Fourier Integral operators modulation spaces short-time Fourier transform Gabor multipliers
2011/9/1
Abstract: A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this princip...
The domain of the Fourier integral
Hilbert spaces of almost periodic functions Fourier transform
2011/3/24
We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space ...
The domain of the Fourier integral
Hilbert spaces of almost periodic functions Fourier transform
2011/3/23
We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space ...
In some previous papers we have defined and studied a ’magnetic’ pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we...