# Extension of the Dirichlet-Jordan convergence Criterion for exponential weights

(2004)

Article

The well-known Dirichlet- Jordan Criterion for Fourier series states that the trigonometric Fourier series of a 2π periodic function f having bounded variation converges to 1/2 [f (x + 0) + f (x - 0)] for every x and this convergence is uniform on every closed interval on which f is continuous (see Theorem 2.8.1 in [3]). We extend this criterion to orthonormal polynomial expansions, and treat the even case of a more general class of exponential weights, on the real line. © 2004 NISC Pty Ltd.