Normed Spaces

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Related lectures (31)

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Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Functional Analysis: Banach and Hilbert Spaces

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

Dual Spaces: Definitions and Properties

Covers the definitions and properties of dual spaces and linear operators.

Normed Spaces: Definitions and Examples

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Functional Analysis and Distribution Theory

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

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.