In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two...

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...

}}{\Big )}} Singular integral operators on closed curves (account of the Sokhotski–Plemelj theorem for the unit circle and a closed Jordan curve) Kramers–Kronig...

second order, and third order; and singular and regular integral equations. These distinctions usually rest on some fundamental property such as the...

the curve decreases as the curve converges to a circular shape, before collapsing to a singularity. If two disjoint simple smooth closed curves evolve...

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...

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...

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 ]...

Cauchy's integral formula. The Poincaré lemma generally fails for singular spaces. For example, if one considers algebraic differential forms on a complex...

theorem is that a Riemannian metric on a closed manifold M determines a real-valued inner product on the integral cohomology of M modulo torsion. It follows...