## Members & Collaborators

## Gama-ini

**The group of Applied Mathematical Analysis, GAMA, **is a team of university researchers specialized in a field of Mathematical Analysis called Approximation Theory. Its aim is the search of approximations to sufficiently general (scalar, vector or matrix) functions by means of other ones belonging to more accessible functional spaces due to their structural characteristics and their computational simplicity. Some examples are approximation by means of polynomial, splines, rational functions, wavelets, etc. All of them appear in numerous applications. From the point of view of basic research we are interested in three aspects:

- Construction of solutions to such problems. Implementation of algorithms for generating such solutions.
- Measuring the rate of convergence of the approximaning functions.
- Algebraic and asymptotic properties of sequences of orthogonal polynomials.

In many of the problems previously pointed out, the ideal approximations are orthogonal projections of the given function on a vector subspace for which we must know orthogonal bases, methods for generating such bases, as well as efficient numerical methods for determining Fourier coefficients. In this case, the development of efficient methods of numeric integration, both on the real line and on the unit circumference arise naturally, which improve the traditional methods of gauss quadrature.

The basic techniques we use are based on harmonic analysis, operator theory, structured matrices (Hankel and Toeplitz among others), function theory (specially, potential theory and special functions).

We constitute a reference group at a national and European level regarding parameters such as publications, organization of events and the participation on scientific committees, as well as in projects of national and international scope (INTAS, bilateral actions and NATO).