On Schrödinger Oscillatory Integrals Associated with the Dunkl Transform
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DOI: 10.1007/s00041-018-9597-3
Abstract: In the paper we study the Schrödinger oscillatory integrals $$T^t_{\lambda ,a}f(x)$$Tλ,atf(x) ($$\lambda \ge 0$$λ≥0, $$a>1$$a>1) associated with the one-dimensional Dunkl transform $${\mathscr {F}}_{\lambda }$$Fλ. If $$a=2$$a=2, the function $$u(x,t):=T^t_{\lambda ,2}f(x)$$u(x,t):=Tλ,2tf(x) solves the free Schrödinger equation… read more here.
Keywords: schr dinger; oscillatory integrals; dunkl transform; dinger oscillatory ... See more keywords
Complexity of oscillatory integrals on the real line
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DOI: 10.1007/s10444-016-9496-6
Abstract: AbstractWe analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space Hs(ℝ)$H^{s} (\mathbb {R})$ and from the space Cs(ℝ)$C^{s}(\mathbb {R})$ with an arbitrary integer s ≥ 1. We find… read more here.
Keywords: real line; oscillatory integrals; mathbb; complexity oscillatory ... See more keywords
Stable application of Filon–Clenshaw–Curtis rules to singular oscillatory integrals by exponential transformations
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DOI: 10.1007/s10543-018-0730-0
Abstract: Highly oscillatory integrals, having amplitudes with algebraic (or logarithmic) endpoint singularities, are considered. An integral of this kind is first transformed into a regular oscillatory integral over an unbounded interval. After applying the method of… read more here.
Keywords: clenshaw curtis; filon clenshaw; oscillatory integrals;
Filon–Clenshaw–Curtis formulas for highly oscillatory integrals in the presence of stationary points
Sign Up to like & getrecommendations! Published in 2017 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2017.02.003
Abstract: Abstract Numerical approximation of a general class of one-dimensional highly oscillatory integrals over bounded intervals with exponential oscillators is considered. A Filon-type method based on modified Clenshaw–Curtis quadrature rules is developed and its stability is… read more here.
Keywords: filon clenshaw; stationary points; oscillatory integrals; highly oscillatory ... See more keywords