Lectures related to Fourier Transform: L^2 Analysis

Explores limits, convergence, and boundedness of functions and sequences.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Covers mathematical concepts from number theory to probability and statistics.

Covers Fourier series, periodic functions, and Fourier transforms.

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

Explores examples of Fourier series coefficients and applications in various functions.

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Explores decreasing and growing functions, bounded sequences, and limit existence.

Explores the continuity of functions in R² and R³, emphasizing accumulation points and limits.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

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

Explores the properties of Fourier transformations, including continuity, linearity, and derivatives.

Covers classical harmonic analysis on the circle, Fourier series convergence, and applications in PDEs.

Explores Fourier transform analysis tools and the importance of computational intelligence in function transformation.

Covers the properties and applications of the Laplace transform in solving differential equations.

Explores the limit of the quotient for sequences and the periodicity of functions.

Explores the properties and applications of the Fourier transform in signal processing and mathematics.

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

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