Differentiating under the integral sign

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

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

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

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

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

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

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

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

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

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