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Related lectures (18)

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Bolzano-Weierstrass Theorem: Sequential Compactness in Hilbert Spaces

Explores the Bolzano-Weierstrass theorem in Hilbert spaces, showcasing sequential compactness and the construction of converging subsequences.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Functional Analysis I: December 16, 2021

Explores digital integration, uniform bounds, weak convergence, and norm homogeneity in functional analysis.

Functional Line: Defining Sequences and Convergence

Covers the definition of the functional line and sequences, emphasizing convergence in functional analysis.

Dual Space and Weak Convergence

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.

Calculus of Variations: Ground States in Quantum Mechanics

Covers the Calculus of Variations to find ground states in quantum mechanics by minimizing energy, discussing the Euler Lagrange equation and the Fundamental Theorem of Young Measure Theory.

Embedding Theorems in Sobolev Spaces

Explores weak convergence, Poincaré inequality, and embedding theorems in Sobolev spaces.

Optimal Transport: Analysis and Proofs

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.