Lecture
The Closed Graph Theorem
Related lectures (34)
Functional Analysis I: Norms and Bounded Operators
Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.
Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Sobolev Spaces in Higher Dimensions
Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.
Functional Analysis I: Operator Definitions
Introduces linear and bounded operators, compact operators, and the Banach space.
Bounded Operators: Theory and Applications
Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.
Weak Formulation of Elliptic PDEs
Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.
Banach-Steinhaus Theorem
Explores the Banach-Steinhaus theorem, uniform boundedness, and operator norms in normed spaces.
Operator Product Expansion
Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.
Extension of Linear Transformations
Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.
Dynamical Approaches to Spectral Theory of Operators
Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.