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FAST DIRECTIONAL COMPUTATION OF HIGH FREQUENCY BOUNDARY INTEGRALS VIA LOCAL FFTs
boundary integral method scattering high frequency waves directional algorithm low-rank approximation Chebyshev interpolation fast Fourier transforms
2015/7/14
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral...
Let C(t) : I 7→ R2 be a simple closed unit-speed C2 curve in R2 with normal ~ n(t). The curve C generates a distribution Γ which acts on vector fields ~ v(x1,x2) : R2 7→ R2 by line integration accordi...
A family of fractional integrals pertaining to multivariable I-function
Fractional integral Eulerian integral
2010/9/25
The object of this paper is to derive an Eulerian integral and a main theorem based upon the fractional operator associated with ¯H -function [3] and multivariable I-function [4] which provide un...
A one parameter family of selfadjoint operators gives rise to a corresponding direct integral. We show how to use the Putnam Kato theorem to obtain a new method for the proof of a spectral averaging r...
Convex Functions and Inequalities for Integrals
Convex functions Measure spaces Lebesgue integrals Banach spaces
2008/7/1
Convex Functions and Inequalities for Integrals.
Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals
Grüss Chebychev and Lupas inequalities Hö lder
2008/7/1
A generalised Chebychev functional involving integral means of functions over different intervals is investigated. Bounds are obtained for which the functions are assumed to be of Hölder type. A ...
Monotonicity Results for a Compound Quadrature Method for Finite-Part Integrals
Hadamard finite-part integral Quadrature formula Product trapezoidal formula Monotonicity Fractional differential equation Discrete Gronwall inequality Backward differentiation formula
2008/6/30
Monotonicity Results for a Compound Quadrature Method for Finite-Part Integrals.
On Some Inequalities of Local Times of Iterated Stochastic Integrals
Continuous local martingale Continuous semimartingale Iterated stochastic integrals Local time Random time Burkholder-Davis-Gundy inequalities Barlow-Yor inequalities
2008/6/27
On Some Inequalities of Local Times of Iterated Stochastic Integrals.
Some bounds for certain highly oscillatory integrals
Oscillatory integrals Filon method error bounds
2010/9/10
The classic standard integration rules usually give inaccurate results for highly oscillatory integrals of the form ∞1 tr−1f(t) sin (αtr)dt, r ≥ 1, where f is any real valued function in C1[1,∞...
Some Oscillatory Singular Integrals on Herz-type Spaces (II)
oscillatory singular integral phase lebesgue space
2007/12/10
In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and...