MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-641
Functional analysis
4Credits ( 3L+1T+0P)
Normal Spaces, continuity of a linear mapping. Banach spaces, Linear Transformations and
functionals and Normed bounded linear transformation, dual spaces, Hahn – Banach theorem.
Hilbert Spaces.
Orthonormal sets, Bessel’s Inequality, Parseval’s relation,
Riesz
Representation theorem, Relationship between Banach Spaces, Hilbert Spaces. Adjoint
operators in Hilbert Spaces, Self adjoint operators, positive operators, Projection Operators
and orthogonal projections in Banach &Hilbert spaces, Fixed point theorems and their
applications, Best approximations in Hilbert Spaces. Gatebux and Frechat Derivatives.
Solution of boundary value problems. Optimization problems. Applications to Integral and
differential equations.
Books Recommended:
1. Functional Analysis-B V Limaye, Wiley Publications
2. Functional Analysis- Brown Page
3. Introductory functional analysis with applications, Kreyszig, Wiley publications