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Averaging over \(N\)-dimensional balls and Cauchy problem for equations of mathematical physics. (English) Zbl 1031.35114

The author considers the averaging over the balls in \(\mathbb{R}^N\). He gives a relation between scale and space dependence of the average function. He also shows connection with equations of mathematical physics.

MSC:

35Q05 Euler-Poisson-Darboux equations
42A85 Convolution, factorization for one variable harmonic analysis
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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