Lectures related to Fourier Inversion Formula

Convergence of Fourier Series

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Trigonometric Polynomials: Fourier Inversion and Plancherel Formulas

Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.

Fourier Transform: Properties and Applications

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Distributions and Derivatives

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Central Limit Theorem

Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.

Fourier Transform: Schwartz Space

Covers the Fourier transform on Schwartz space and its properties, including continuity and linearity, as well as the density of smooth compactly supported functions.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Fourier Inversion Formula and Plancherel Identity

Covers the Fourier inversion formula and the Plancherel identity, emphasizing their importance in mathematical analysis.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Signal Representations

Covers the properties of signal/data representations using Fourier transformations and matrices.