In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two...
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T^{t}(b_{2}),} is in BMO, where Tt is the transpose operator of T. Singular integral operators on closed curves Stein, Elias (1993). "Harmonic Analysis". Princeton...
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second order, and third order; and singular and regular integral equations. These distinctions usually rest on some fundamental property such as the...
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}}{\Big )}} Singular integral operators on closed curves (account of the Sokhotski–Plemelj theorem for the unit circle and a closed Jordan curve) Kramers–Kronig...
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that is, a function F such that F′ = f on the interval. Provided the integrand and integral have no singularities on the path of integration, by the fundamental...
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integral theorem, one can show that the integral over C (or the closed rectifiable curve) is equal to the same integral taken over an arbitrarily small circle...
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the curve decreases as the curve converges to a circular shape, before collapsing to a singularity. If two disjoint simple smooth closed curves evolve...
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that the plane curve Y 2 = X 3 {\displaystyle Y^{2}=X^{3}} has a singularity at the origin. Another domain that is not integrally closed is A = Z [ 5 ]...
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Poincaré lemma (section On singular spaces)
resolution of the constant sheaf R M {\displaystyle \mathbb {R} _{M}} on M. The singular cohomology of a contractible space vanishes in positive degree, but...
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include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have...
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