### Analysis

Mathematical Analysis initially developed from arguments needed in the infinitesimal study of geometrical objects and physical motions. After the great success of the heroic age of differential and integral calculus, it was realized that, by focusing attention not on a single function in isolation, but rather on an appropriate class of functions, one could obtain a better understanding and an expansion of the classical theories. Thus, Functional Analysis was born about a century ago, with great benefits to several areas of modern mathematics and many remarkable applications to the natural sciences.

The faculty listed by our department as analysts are actually all functional analysts. They like to work in infinite dimensional spaces (of functions, operators, representations, dynamical systems). Among their main objectives are the solution of equations, minimization of functionals, and classification and study of algebras of operators. The numerous applications vary from classical problems of continuum mechanics and information theory to image analysis, knot theory and quantum computing.

Several research seminars devoted to such subjects are organized all year around. They are attended by many of our graduate students and attract many distinguished visitors.

#### Faculty

**Charles A. Akemann****PhD:**University of California, Berkeley, 1966**Interests:**Functional Analysis**Office:**Room 6706**email:**akemann@math.ucsb.edu

**Gustavo Ponce****PhD:**The Courant Institute, 1982**Interests:**Non-linear PDE's**Office:**Room 6505**email:**ponce@math.ucsb.edu

**Mihai Putinar****PhD:**University of Bucharest, 1984**Interests:**Complex analysis, operator theory**Office:**Room 6722**email:**mputinar@math.ucsb.edu

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