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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 TECHNIQUE FOR UPDATING HIERARCHICAL SKELETONIZATION-BASED FACTORIZATIONS OF INTEGRAL OPERATORS
factorization updating local perturbations hierarchical factorizations integral equations
2015/7/14
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geo...
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...
Uncertainty principles for integral operators
Uncertainty principles annihilating pairs Dunkl transform Fourier-Clifford transform integral operators
2012/6/25
The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of...
A T(1)-Theorem for non-integral operators
T (1)-Theorem T (b)-Theorem paraproducts Davies-Gaffney estimates Hardy and BMO spaces
2011/9/16
Abstract: Let $X$ be a space of homogeneous type and let $L$ be a sectorial operator with bounded holomorphic functional calculus on $L^2(X)$. We assume that the semigroup $\{e^{-tL}\}_{t>0}$ satisfie...
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...
Stability of Localized Integral Operators on Weighted $L^p$ spaces
Integral operator weighted function space Muckenhoupt weight spectrum Bessel potential infinite matrix Wiener’s lemma
2011/8/31
Abstract: In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is t...
Bounds on oscillatory integral operators based on multilinear estimates
oscillatory integral operators multilinear estimates
2011/2/22
Let S ⊂ Rn be a smooth, compact hyper-surface with positive definite second fundamental form. Let σ be its surface measure.We prove the following result with respect to the Fourier restriction/e...
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...