In this paper we present an analytic treatment of the inverse problem of reconstructing the internal electric conductivity of an in nite domain (the lower half space) from electrical measurements performed on its surface. To this end we transform the initial di erential equation into an integral equation, a procedure which has the advantage of permitting a simple discussion of the regularizatio...

We demonstrate that for the sine-Gordon theory at the free fermion point, the 2point correlation functions of the fields exp(iαΦ) for 0 < α < 1 can be parameterized in terms of a solution to a sinh-Gordon-like equation. This result is derived by summing over intermediate multiparticle states and using the form factors to express this as a Fredholm determinant. The proof of the differential equa...

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

may be reduced to a single linear integral equation whose kernel is defined on a^x^a+n(b — a), a^s^a+n(b — a). Greggi§ considered a system of the form (1) and by use of the transformation introduced by Fredholm showed the form of the resolvent matrix for the system; for the symmetric system where Ku(x; s) =Kn(s; x) (i,j = \,2, ■ ■ ■ , n) he also stated theorems analogous to those proved by Schm...

The problem of global illumination in computer graphics is described by a Fredholm integral equation of the second kind. Due to the complexity of this equation, Monte Carlo methods provide an efficient tool for the estimation of the solution. A new approach, using quasi-Monte Carlo integration, is introduced and compared to Monte Carlo integration. We discuss some theoretical aspects and give n...

In potential theory, the boundary element method is recognized as a powerful numerical tool. Usually it works with the simple fundamental solution based on the wholeor half-space scalar Green function. In the case of a uniform and isotropic domain connected only to isolated regions, a Fredholm integral equation of the second kind with respect to the potential can be derived [l, 21 which is solv...

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by con...

We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

The numerical evaluation of the transforms in the title, and their inverses, is considered, using a variety of decomposition, truncation, and quadrature methods. Extensive numerical testing is provided and an application given to the numerical evaluation of the kernel of a Fredholm integral equation of interest in mixed boundary value problems on wedge-shaped domains. AMS subject classification...