Functional Calculus and Borel Transform

Related lectures (32)

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Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Explores the matrix representation of operators and basis transformation in linear algebra.

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

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

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

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

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

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

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.