A note on Mathieu functions

The Tabulation of Mathieu Functions

and in which a and 6 are constants, arises in applied mathematics in two main groups of problems. The first group, of which Mathieu's problem of the transverse vibrations of a taut elliptic membrane is typical, consists of boundary problems relative to some partial differential equation, such as the wave equation, where the boundary is an ellipse—or possibly a hyperbola. Here a fundamental requ...

A Note on Conjugate Functions

1. Statement of results. The purpose of this note is to discuss as simply as possible a generalization of the classical theorem of M. Riesz2 on the integrability of the conjugate functions of functions in LP, and to point out some of the consequences for Fourier series. Suppose that(t) is a non-negative, convex function defined for t^O with (2t) ̂K<p(t) ior some constant K. Th...

A Note on Convex Functions

In this paper, we give twoweak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

A Note on SpanP Functions

A Note on Recursive Functions

In this paper, we propose a new and elegant deenition of the class of recursive functions, analogous to Kleene's deenition but diiering in the primitives taken, thus demonstrating the computational power of the concurrent programming language in-The deenition can be immediately rephrased for any distributive graph in a count-ably extensive category with products, thus allowing a wide, natural g...