Table of Contents

**MTH641: Functional Analysis**

Functional analysis is a branch of mathematical analysis, the essence of which is formed by the study of vector spaces given a certain type of boundary-related structure (e.g., internal product, standard, topology, etc.) and line functions defined in these spaces. and to respect these buildings in a proper manner. MTH641 Handouts pdf

## MTH641 Handouts pdf

**Course Category: Mathematics **

**Course Outline**

Introduction, Metric space, subspace, Triangle inequality, Axioms of a metric, Sequence space, Space B(A) of bounded functions, Some Inequalities, Ball and sphere, Continuous 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 on Finite-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. MTH641 Handouts pdf

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### MTH641 HANDOUTS

**MTH641: Functional Analysis**

The branch of mathematics analysis is responsible for jobs, or job responsibilities. It emerged as a distinct field in the 20th century, when it was realized that various mathematical processes, from arithmetic to arithmetic processes, exhibited very similar characteristics. A function, like a function, is a relationship between objects, but objects can be numbers, vectors, or functions.