Abstract
A generalized version of local regularization is developed. The convergence criteria set forth in the generalization are shown to be realized naturally by a particular local regularization scheme when applied to finitely-smoothing linear Volterra convolution equations in the Banach spaces L-p(0, 1), 1 <= p <= infinity. The method leads to convergence with a priori parameter selection for 1 < p < infinity and under assumptions of increased regularity of the true solution for 1 <= p <= infinity. Rates of convergence are established beyond those previously known for local regularization of this problem in C[0, 1] and under more general source conditions. Numerical examples are included to illustrate implementation and effectiveness of the method.