Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2010, Article ID 570136, 8 pages doi:10.1155/2010/570136 Research Article Application of Periodized Harmonic Wavelets towards Solution of Eigenvalue Problems for Integral Equations Carlo Cattani 1 and Aleksey Kudreyko 2 1 diFarma, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy 2 Department of Mathematics and Computer Science, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy Correspondence should be addressed to Aleksey Kudreyko, akudreyko@unisa.it Received 12 October 2009; Accepted 19 November 2009 Academic Editor: Alexander P. Seyranian Copyright q 2010 C. Cattani and A. Kudreyko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article deals with the application of the periodized harmonic wavelets for solution of integral equations and eigenvalue problems. The solution is searched as a series of products of wavelet coefficients and wavelets. The absolute error for a general case of the wavelet approximation was analytically estimated. 1. Introduction Mathematical models describe a variety of physical and engineering problems and processes which can be represented by integral equations IEs. The homogeneous Fredholm IE is written as follows: λf x -  b a Kx, tf tdt  0, 1.1 where a and b are finite numbers, the kernel Kx, t is known function, and λ and f x are the unknown eigenvalue and associated eigenfunction. Equation 1.1 has a nontrivial solution only for some values of λ. There exist two different methods to solve IEs numerically. The first one is to expand the equation by the appropriate set of basis functions, such as the classical orthogonal polynomials 1 or wavelets e.g. 2, 3, and to reduce the equation to simultaneous