The Analysis group works on various aspects of Functional Analysis, namely Matrix analysis, Birkhoff-James orthogonality, operator theory, frame theory, the geometry of Banach spaces, and function spaces, with applications to optimization, approximation theory, and distance problems. The faculty members’ work is also reflected in the study of special matrices and their positivity properties, Hardy spaces, Reproducing Kernel Hilbert spaces, C*-algebras, Hilbert C*-modules, etc.

Applications:

Operator theory on Hilbert spaces provides a natural framework for problems in Quantum mechanics and Control theory. Some problems in geophysical imaging lead to investigations of certain classes of operators in Hardy spaces. RKHS is used in Machine learning and Statistical Analysis of time series.