Approximation theorems for double orthogonal series, II

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Inverse Approximation Theorems for . . .

A Consistency Condition for the Double Series Approximation Method

The double series approximation method of Bonnor is a means for examining the gravitational radiation from an axisymmetric isolated source that undergoes a finite period of oscillation. It involves an expansion of the metric as a double Taylor series. Here we examine the integration procedure that is used to form an algorithmic solution to the field equations and point out the possibility of th...

Steinitz Theorems for Simple Orthogonal Polyhedra

We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By analogy to Steinitz’s theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric pro...

Ergodic Theorems and Approximation Theorems with Rates

A-ergodic nets and A-regularized approximation processes of operators are introduced and their convergence theorems are discussed. There are strong convergence theorems, uniform convergence theorems, theorems on optimal convergence, and theorems on non-optimal convergence and its sharpness. The general results provide unified approaches to investigation of convergence rates of ergodic limits an...