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Related lectures (13)

Convolution and Fourier Transform

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

Spatial Topological Queries

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

Interior Regularity Results

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

Functional Analysis and Distribution Theory

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

Analysis IV: Tempered Distributions and Dirac Functional

Introduces tempered distributions, derivatives, and Dirac functional in analysis.

Fourier Transform of Tempered Distributions: Reflection and Translation

Explores the Fourier transform of tempered distributions, emphasizing reflection and translation operations.

Operations on Distributions and Fourier Transform Properties

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

Distributional Derivatives

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

Functional Analysis and Distribution Theory

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

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.

Stochastic Gradient Descent: Optimization and Convergence Analysis

Explores Stochastic Gradient Descent for non-strongly convex functions and the impact of step size on convergence.

Uniqueness of Fourier Representations

Explores the uniqueness of Fourier representations for continuous functions, demonstrating that coefficients must be equal if two valid series exist.

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