MATH-405: Harmonic analysis

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Lectures in this course (10)

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Harmonic Analysis: Schwerte Functions

Explores Schwerte functions in harmonic analysis, emphasizing compact support and function convergence.

Approximate Identities in Harmonic Analysis

Explores the concept of approximate identities in harmonic analysis and their applications in mathematical settings.

Harmonic Analysis: Properties and Consequences

Explores properties and consequences in harmonic analysis, including density and convergence.

Spectral Theory: Regularity and Embedding

Explores spectral theory, emphasizing regularity properties and embedding theorems in the context of Sobolev spaces and compactly supported functions.

Wayl's Theorem: Polynomial Clarity

Focuses on the proof of Wayl's theorem through polynomial manipulation and induction.

Harmonic Analysis: Classical Theory and Fourier Series

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

Uniqueness of Fourier Representations

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

Hilbert Transform: Exercises and Key Lemmas

Covers exercises and key lemmas related to the Hilbert transform.

Sequence Uniformity: Convergence and Squeeze Theorem

Explores sequence uniformity, convergence, and the Squeeze Theorem in mathematical analysis.

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