I am a member of the Department of Applied Mathematics at Santa Clara University.

    My research work focuses on Harmonic Analysis and its applications to the study of singular operators, Partial Differential Equations, Spectral Theory, signal processing, and the development of Numerical Methods for the fast evaluation of dense matrices. 

    Harmonic Analysis is the mathematical theory of oscillations. A key concept in the field is that functions can often be represented as a sum of  waves that vibrate at different frequencies and so, they are in essence mutually orthogonal. 

    Examples of such waves include plane waves (also called harmonics, which are used in Fourier Analysis), Gabor frames, wavelet systems (such as Haar, Daubechies, Meyer, or Shannon wavelets), wave packets, chirplets, Littlewood-Paley decompositions and other frequency projections, Rademacher or Walsh systems, and in general, eigenfunctions of a differential operator with different energy levels. These methods to decompose functions can then be used to solve a large variety of problems in Mathematics, Science, and Engineering.

Contact information:
        Santa Clara University, Heafey Hall, bldg. 202, office 117
        500 El Camino Real, Santa Clara, CA 95053

        Email: paco.villarroya@scu.edu

        MySCUwebsite