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MTH641 : Functional Analysis

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Dr. Sarfraz Ahmad
Post Doctorate Combinatorics & Commutative Algebra
Philipps-Universität Marburg, Germany

Course Contents

Introduction, Metric space, subspace, Triangle inequality, Axioms of a metric, Sequence space, Space B(A) of bounded functions, Some Inequalities, Ball and sphere, Continnous mapping, accumulation point, Dense set, separable space, Convergence of a sequence, limit, Cauchy sequence, completeness, Real line, complex plane, Uniform convergence, Discrete metric, Isometric mapping, isometric spaces, Homeomorphism, Normed Space, Banach Space, Further Properties of Normed Spaces, Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite Dimension, Linear Operators, Bounded and Continuous Linear Operators, Linear Functional, Linear Operators and Functional onFinite Dimensional Spaces, Normed Spaces of Operators, Dual Space, Inner Product Space, Hilbert Space, Further Properties of Inner Product Spaces, Orthogonal Complements and Direct Sums, Orthonormal Sets and Sequences, Series Related to Orthonormal Sequences and Sets, Total Orthonormal Sets and Sequences, Legendre Hermite and Laguerre Polynomials, Representation of Functional on Hilbert Spaces,  Hilbert Adjoint Operator, Self-Adjoint, Unitary and Normal Operators.