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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Approximate identities and pointwise convergence
There is an answer to this question in the book of Folland:
Folland, Gerald B. Real analysis: modern techniques and their applications. Vol. 40. John Wiley and Sons, 1999.
8.15 Theorem. Suppose $|\phi …