Decomposition of spectrum (functional analysis)

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Calculus of Variations: Radon-Nikodym Theorem

Covers the Radon-Nikodym theorem and the uniqueness of signed Borel measures.

Non-Bounded Operators: Spectral Theory

Explores the spectral theory of non-bounded operators and the importance of closed operators for spectral decomposition.

Functional Calculus: Self-Adjoint Operators

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Laplacian Matrix in Networked Control Systems

Explores the Laplacian matrix in electric and mechanical networks, consensus, and properties of Laplacian matrices in networked control systems.

Conditional Entropy and Data Compression Techniques

Discusses conditional entropy and its role in data compression techniques.

Signals & Systems II: Convolution Stability and Operators

Explores convolution stability, LID operators, and the Z-transform properties.

Synchrotron Radiation

Covers the properties of synchrotron radiation, including its emission by relativistic particles and its effect on the beam through radiation damping.

Proof of Weyl's Theorem

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.