Wavelets: Properties and approximate solution of a second kind integral equation

In this paper, we show that, under some conditions, a wavelet basis of L2(R) can be used as a tool for the uniform approximation in the space Cα (R) ∩ L2(R), α > 0, where Cα (R) denotes the Hölder space of exponent α. As a result of this property, we give a numerical application of wavelets. This application is a wavelet-based method for the numerical solution of a Redholm equation of the second kind with solution lying in C0α (R), the Hölder space of compactly supported functions with Hölder exponent α > 1/2.