Fourier Analysis: Applications and Inversion Formula

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Lebesgue Measure and Fourier Analysis

Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.

Wave Propagation: General Solutions

Explores the general solutions for wave propagation and Fourier transforms in periodic functions.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Fourier Analysis: Fourier Series and Transform

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Fourier Transform and Schwartz Space

Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.

Ewald Summation: Long-Range Interaction and Self-Interaction Correction

Explains Ewald summation, self-interaction correction, and short-range interaction calculations.

Inverse Fourier Transform: Verification and Properties

Focuses on the inverse Fourier transform, verification, and properties.

Spectral Properties of Fourier Series and Fourier Transforms

Explores the motivation behind Fourier series and transforms, their fundamentals, and applications in solving differential equations.

Fourier Series and Transforms: Introduction and Properties

Covers Fourier series, Fourier transforms, and convolution properties, including linearity and commutativity.

Signal Representation: Fourier Transforms

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