Lecture

Lecture 4: Hilbert Spaces and Unique Solutions

Related lectures (31)

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Delves into the completeness of Lp spaces and the density of function classes in L².

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers the states of composite systems in Hilbert space, including operators, observables, tensor products, eigenvalues, and partial measurements.

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Explains the postulates of quantum mechanics, including system description, evolution, measurement, composite systems, and examples with qubits.

Explores interior regularity results, focusing on weak solutions and unique selection in mathematical analysis.

Explores the addition of angular momenta in quantum mechanics and delves into Bell's Theorem.

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Covers various examples of function spaces and linear applications between them.

Covers Advanced Quantum Field Theory with a focus on spinors, wave functions, rotations, and constraints.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Offers a crash course on quantum mechanics, covering vector spaces, superposition, observables, and self-adjoint operators.

Covers the review of function spaces and explores the concept of compact operators.