A Sequence of Piecewise Orthogonal Polynomials (I) (Linear Case).

Abstract : This paper considers a sequence of piecewise linear orthogonal functions (U sub i) which is complete in L sub 2. Explicit expressions for the U sub i are given. Any continuous function can be expanded in a series of constant multiples of functions U sub i under the sense of uniform convergence by group. While the partial sum of the corresponding expression for a continuous function may fail to converge uniformly, a certain subsequence does. (Author)