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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...
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...
Commutants of composition operators on the Hardy space of the disk
Composition operator Commutant Hardy space
2015/1/19
The main part of this thesis, Chapter 4, contains results on the commutant of a semigroup of operators defined on the Hardy Space of the disk where the operators have hyperbolic non-automorphic symbol...
D-bar and Dirac Type Operators on Classical and Quantum Domains
Dirac Operators Noncommutative Geometry
2015/1/19
I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the in...
Order continuous operators on CD0(K,E) and CDw(K,E)-spaces
CD0(K)-spaces order continuous operators isometric lattice isomorphism
2011/4/6
In [2], Alpay and Ercan characterized order continuous duals of spaces CD0(K, E) and CDw(K, E) where K is a compact Hausdorff space without isolated points and E is a Banach lattice. In this note, we ...
Graphs of Hecke operators
Graphs Hecke operators
2011/2/21
Let X be a curve over F q with function field F. In this paper, we define a graph for each Hecke operator with fixed ramification. A priori, these graphs can be seen as a convenient
language to organ...
D-branes, surface operators, and ADHM quiver representations
D-branes surface operators ADHM quiver representations
2011/3/2
A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge the-ories using D-brane engineering.
Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
Asymptotic ergodicity eigenvalues of random operators localized phase
2011/1/18
We prove that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of N. Minami (see [24]). N. Minami conj...
Weighted composition operators on weighted vector-valued Bergman spaces
weighted composition operator vector-valued Bergman spaces
2010/9/26
In this paper we first introduce weighted vector-valued Bergman spaces ,
Λ of the upper half-plane. We then discuss their basic propertie...
Weighted composition operators between weighted Bergman-Nevanlinna and Bloch-type spaces
weighted composition operator Bloch-type spaces
2010/9/26
In this paper, we characterize the boundedness and compactness of weighted composition operators , ...
Hereditarily indecomposable, separable L_\infty spaces with \ell_1 dual having few operators, but not very few operators
Hereditarily indecomposable math
2010/11/24
Given a natural number $k \geq 2$, we construct a hereditarily indecomposable, $\mathscr{L}_{\infty}$ space, $X_k$ with dual isomorphic to $\ell_1$. We exhibit a non-compact, strictly singular operato...
Some estimates for Bochner-Riesz operators on the weighted Morrey spaces
Bochner-Riesz operators the weighted Morrey spaces
2010/11/12
In this paper, we will obtain some weighted strong type and weak type estimates of Bochner-Riesz operators $T^{{(n-1)}/2}_R$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ for $1\le p<\infty$ and $0...