Fourier Series: Extension and Periodicity

Related lectures (28)

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Explores differentiating under the integral sign and continuity of functions in integrals.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

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

Covers the properties of harmonic functions and the concept of mollification.

Covers the isomorphism of coverings and the lifting theory.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

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