Advanced-analysis-ii

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Related lectures (30)

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Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Normed Spaces & Reflexivity

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

The Banach Fixed Point Theorem

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Interpolation Spaces

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Definition of Sobolew Spaces

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Functional Analysis: Banach and Hilbert Spaces

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.