Functional Calculus and Borel Transform

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Covers the fundamental concepts of unbounded operators in quantum physics, focusing on defining a functional calculus and spectral decomposition.

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

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

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

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Explains the postulates of quantum mechanics and the representation of observables by operators.

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Covers the proof of unitary group uniqueness and spectral types.