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Lecture
Dual Space and Weak Convergence
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Functional Analysis: Banach and Hilbert Spaces
Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.
Weak Convergence in Hilbert Spaces
Explores weak convergence in Hilbert spaces, discussing definitions, implications, and examples.
Distributions & Interpolation Spaces
Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.
Function Spaces and Hilbert Spaces
Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.
Causal Systems & Transforms: Delay Operator Interpretation
Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.
Bounded Operators: Theory and Applications
Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.
Linear Applications: Bases and Dual Spaces
Explores bases, dual spaces, and linear applications in linear algebra.
Postulates of Quantum Mechanics
Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.
Linear Forms in Vector Spaces
Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.
Quantization: Topological Operators
Covers the quantization of topological operators and Ising models on square lattices.