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Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
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...
Integral geometry of complex space forms
Integral geometry complex space forms Differential Geometry
2012/4/18
Using the language of Alesker's theory of valuations on manifolds, a thorough account of the integral geometry of the complex space forms is given. The local kinematic formulas on complex space forms ...
Sets avoiding integral distances
excluded distances Euclidean Ramsey theory integral distances Erdos-type problems
2012/4/18
We study open point sets in Euclidean spaces $\mathbb{R}^d$ without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper d...
Integral estimates for the trace of symmetric operators on complete submanifolds
Integral estimates trace of symmetric operators complete submanifolds Differential Geometry
2012/4/17
Let $\Phi:TM\to TM$ be a positive-semidefinite operator of class $C^1$ defined on a complete noncompact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given condi...
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).
Lifting, restricting and sifting integral points on affine homogeneous varieties
integral points affine homogeneous varieties
2010/12/13
In [GN2] an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean e...