Concept
Functional analysis
Related lectures (101)
Operator Product Expansion
Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.
Numerical Approximation of PDEs
Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.
Weak Derivatives: Definition and Properties
Covers weak derivatives, their properties, and applications in functional analysis.
Signals and Systems I: Fourier Transform and Spectral Analysis
Explores Fourier series, energy calculation, functional spaces, correlation spectra, and spectral density in signals and systems.
Dual Space and Weak Convergence
Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.
Interpolation Spaces
Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.
Quantum Field Theory: Ward Identities
Explores Ward identities in Quantum Field Theory, emphasizing classical and quantum cases, symmetry generators, and perturbation theory.
Signals and Systems II: Statistical Properties and Signal Representation
Explores statistical properties, signal representation, discrete signals, and binary signals.
Signal Processing: Basics and Spectral Analysis
Covers the basics of signal processing, linear estimation, and digital filters.
Distributions and Derivatives
Covers distributions, derivatives, convergence, and continuity criteria in function spaces.