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Functional analysis
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Related lectures (32)
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The Closed Graph Theorem
Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.
Operator Projections: Characteristic Functions
Covers the concept of operator projections onto subspaces, focusing on characteristic functions.
Quantum Field Theory: Ward Identities
Explores Ward identities in Quantum Field Theory, emphasizing classical and quantum cases, symmetry generators, and perturbation theory.
Quantum Dynamics: Trajectory-Based Solutions
Explores quantum dynamics with trajectories and their applications in nonadiabatic dynamics and coupling with external fields.
Signals and Systems II: Statistical Properties and Signal Representation
Explores statistical properties, signal representation, discrete signals, and binary signals.
Cauchy Test and Generators
Explores Cauchy test, generators, and density in functional analysis.
Signal Processing: Basics and Spectral Analysis
Covers the basics of signal processing, linear estimation, and digital filters.
Functional Analysis and Distribution Theory
Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.
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.
Bilinear Forms: Theory and Applications
Covers the theory and applications of bilinear forms in various mathematical contexts.