Non-Bounded Operators: Spectral Theory

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Page 2 of 4

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

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

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.