Note on a singular integral

A Note on Calderón-zygmund Singular Integral Convolution Operators

Note on Singular Integrals1

then by a well-known theorem of M. Riesz, ll/(*)IU<^ll/(*)IU ifi<#<«. Hardy and Littlewood [4], and Babenko [l], have complemented this result by proving that: \\f(x)\x\e\\p<Ap.f!\\f(x)\x\e\\P, if l<p< co, and -l/p<P<l/p'. The theory of conjugate functions has been extended to w-dimensions by A. P. Calderon and A. Zygmund. In [2] and [3] they have considered a wide variety of singular transform...

A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebys...

A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provid...

Note on Integral Distances

A planar point set S is called an integral set if all the distances between the elements of S are integers. We prove that any integral set contains many collinear points or the minimum distance should be relatively large if |S| is large.