Lectures related to Distribution (mathematics)

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

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Probability Theory: Random Variables and Distributions

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Quadratic Forms and Hecke Operators

Explores quadratic forms, Hecke operators, eigenvalues, and compactly supported functions in matrix theory.

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Martingales and Brownian Motion: Reflection Principle

Explores the reflection principle in martingales and Brownian motion, simplifying probability calculations.

Distributional Derivatives

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

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Probability and Statistics

Explores joint random variables, conditional density, and independence in probability and statistics.

Operations on Distributions and Fourier Transform Properties

Explores new operations on tempered distributions and their compatibility with functions.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Interior Regularity Results

Explores interior regularity results, focusing on weak solutions and unique selection in mathematical analysis.

Probability Distributions: Moments and Transformations

Explores the bijection between distribution functions and moment generating functions.

Introduction to Distributions

Covers Green's representation formula, fundamental solutions, and distribution properties.

Spatial Topological Queries

Explores topology, test functions, and space operators for spatial queries.

Brownian Motion: Fundamentals and Applications

Explores the fundamentals of Brownian motion, including particle positions and distribution functions.