Convolution and Fourier Transform

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Related lectures (31)

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Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Distributions and Derivatives

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

Normed Spaces

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

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Heat and Wave Equations: Analysis IV

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Extension of Linear Transformations

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

Functional Analysis and Distribution Theory

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

Equations of Heat and Fourier Transform

Covers heat equations, Fourier transforms, and variable separation methods.

Free Propagation and Heat Equation

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.