We construct gauge invariant operators for singular knots in the context of Chern-Simons gauge theory. These new operators provide polynomial invariants and Vassiliev invariants for singular knots. As an application we present the form of the Kontsevich integral for the case of singular knots. CERN-TH/97-360 December 1997

In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix. As in the prequel, where we considered the eigenvalues of Hermitian matrices, the non-ra...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement comp...

In this paper we pursue the study of the problem of controlling the maximal singular integral T ∗f by the singular integral Tf . Here T is a smooth homogeneous Calderón-Zygmund singular integral of convolution type. We consider two forms of control, namely, in the L2(Rn) norm and via pointwise estimates of T ∗f by M(Tf) or M2(Tf) , where M is the Hardy-Littlewood maximal operator and M2 = M ◦M ...

We derive certain estimates and asymptotics for oscillatory integral operators with degenerate phase functions, concentrating our attention on the situation when one of the projections from the associated canonical relation is a Whitney fold. We discuss related topics: convexity, higher order degeneracy of canonical relations, and almost orthogonality. In the second part of the paper, we apply ...

This paper concerns the integral equation

In [21] this theorem is used by L. v. Wolfersdorf to consider singular integral equations on the real halfline involving the singular (complex) Hilbert operator. This theory is extended by Askabarov in [1] to the complex case. We want to investigate a special family of singular integral operators in Clifford analysis which has in IR an application to the nonlinear magnetic field equation ([5]) ...

Eleonor Harboure Beairiz Viviani Presentado pOl" Carlos Segovia Abstract: We study the boundedness of singular integral operators on Orlicz-Hardy spaces H w , in the setting of spaces of homogeneous type. As an application of this result, we obtain a characterization of HwIRn in terms of the Riesz Transforms. § 1. NOTATION AND DEFINITIONS Let X be a set. A function d : X x X -+ IR+ U {OJ shall ...

We consider singular perturbation elliptic problems depending on a parameter ε such that, for ε = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro Lopatinskii condition). The limit only holds in very abstract spaces out of distribution theory involving complexification and non-local phenomena. We give a very elementary model problem showing the main fea...