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.
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RESEARCH FIELDS
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Algebra
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Analysis
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Applied
Math
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Geometry
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Number
Theory
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PDE
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Topology
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Faculty

Charles A. Akemann
PhD: University of California at Berkeley, 1966
Interests: Functional Analysis
Office: Room 6706
akemann-A.T-math.ucsb.edu

Gustavo Ponce
PhD: The Courant Institute, 1982
Interests: Non-linear PDE's
Office: Room 6505
ponce-A.T-math.ucsb.edu

Mihai Putinar
PhD: University of Bucharest, 1984
Interests: Complex analysis, operator theory
Office: Room 6722
mputinar-A.T-math.ucsb.edu
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Visiting Faculty
No Visiting Faculty at this time.