One of the earliest attempts to rigorously prove the solvability of Dirichlet’s boundary value problem was based on seeking the solution in the form of a ”potential of double layer”, and this leads… (More)

We consider the Dirichlet problem for the Laplace operator with rational data on the boundary of a planar domain. Our main results include a characterization of the disk as the only domain for which… (More)

Hamming considered the problem of efficient, faultless transmission of binary data over a noisy channel. For a channel which corrupts no more than one binary digit in each sequence of length n, he… (More)

In this work we develop the family of Prometheus orthonormal sets (PONS) in the framework of certain abelian group algebras. Classical PONS, considered in 1991 by J. S. Byrnes, turned out to be a… (More)

Introduction. In harmonic analysis, it is important to know how various properties of a function on R reflect themselves as restrictions on its spectrum, i.e., the support of its (distributional)… (More)

A typical result (consequence of Theorem 1) is that if such a function tends to a limit X as x—»x° from inside an open cone with vertex at x°, then it tends "on the average" to X as x—>x° from inside… (More)

1. Introduction. A question that has been discussed in recent years is that of parallel computation. Can a given computation be broken up into independent assignments which may be performed… (More)

In 1934 H. Malmheden [15] discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin [7] 23 years later, it… (More)