Functional Analysis and Distribution Theory

Related lectures (32)

Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.

Explores functional spaces, linear applications, sublinear functionals, and the Hahn-Banach theorem.

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Covers the Cayley-Hamilton Theorem, stating that for a linear operator on a vector space, its characteristic polynomial satisfies its own equation.

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

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

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Covers the Hessian and Newton's method for optimization using iterative processes.

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.

Covers the concept of linear operators, focusing on traces and boundedness.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

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