منابع مشابه
Principal Value Integrals
A general uniform convergence theorem for numerical integration of Cauchy principal value integrals is proved. Seven special instances of this theorem are given as corollaries.
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Inspired by p-adic (and real) principal value integrals, we introduce motivic principal value integrals associated to multi-valued rational differential forms on smooth algebraic varieties. We investigate the natural question whether (for complete varieties) this notion is a birational invariant. The answer seems to be related to the dichotomy of the Minimal Model Program.
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Principal value integrals are associated to multi–valued rational differential forms with normal crossings support on a non–singular algebraic variety. We prove their vanishing on rational surfaces in the context of a conjecture of Denef–Jacobs. As an application we obtain a strong vanishing result for candidate poles of p–adic and motivic Igusa zeta functions.
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Consider the Cauchy principal value integral I(kf;X)=i k{x)F^Ldx, -1<A<1. 7-1 x — A If we approximate f(x) by Yli=oajP¡(x'i w) where {p } is a sequence of orthonormal polynomials with respect to an admissible weight function w and û, = (/. P.), then an approximation to I(kf; X) is given by X!/=o ajl(kp¡ ; ^)If, in turn, we approximate a¡ by ajm = £TM , wimf(x¡m)Pj(xim), then we get a double seq...
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Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using n + 2 points which requires only values of the integrand. However, this new rule does not exist for all n...
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ژورنال
عنوان ژورنال: Monatshefte f�r Mathematik
سال: 2000
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s006050070027