Unitary Group and Spectral Types

Related lectures (32)

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Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

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

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

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

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

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