Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase
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DOI: 10.1007/s10114-019-8270-3
Abstract: In this paper, the weak (1,1) boundedness of oscillatory singular integral with variable phase P(x)γ(y) for any x, y ∈ ℝ, $$Tf(x)\;:=\;{\rm{p}}.\>{\rm{v}}.\>\int_{- \infty}^\infty {{{\rm{e}}^{{\rm{i}}P(x)\gamma (y)}}f(x\;-\;y)\frac{dy}{y}}$$ is studied, where P is a real monic polynomial on… read more here.
Keywords: variable phase; integral variable; weak boundedness; singular integral ... See more keywords
Numerical evaluation of oscillatory-singular integrals
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2019.1572884
Abstract: ABSTRACT In this paper, we consider an asymptotic Filon-type method for computing the oscillatory Cauchy principal value integrals and end-point oscillatory-singular integrals. The method is constructed by using a Lagrange interpolating polynomial to approximate the… read more here.
Keywords: evaluation oscillatory; numerical evaluation; singular integrals; oscillatory singular ... See more keywords