Unitary Group and Spectral Types

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Related lectures (32)

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Functional Calculus: Operator Definition and Properties

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

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Spectral Decomposition of Bounded Self-Adjoint Operators

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

Linear Algebra: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, including states, observables, composite systems, Schrödinger equation, and entangled states.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

Markov Chains Decomposition

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

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