Voldřich, Josef Averaging over \(N\)-dimensional balls and Cauchy problem for equations of mathematical physics. (English) Zbl 1031.35114 J. Math. Anal. Appl. 272, No. 2, 582-595 (2002). 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. Reviewer: Khalifa Trimèche (Tunis) 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 Keywords:averaging; Cauchy problem; Euler-Poisson-Darboux equation PDFBibTeX XMLCite \textit{J. Voldřich}, J. Math. Anal. Appl. 272, No. 2, 582--595 (2002; Zbl 1031.35114) Full Text: DOI References: [1] Holeček, M., Heat conduction equations as the continuum limits of scale dependent hydrodynamic theory, Phys. A, 183, 236-246 (1992) [2] Kufner, A.; John, O.; Fučı́k, S., Function Spaces (1977), Academia: Academia Prague [3] Prudnikov, A.; Brychkov, Y.; Marichev, O., Integrals and Series (1983), Nauka: Nauka Moscow, in Russian · Zbl 0626.00033 [4] Schwartz, L., Méthodes mathématiques pour les sciences physiques (1965), Hermann: Hermann Paris [5] Stein, M.; Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces (1971), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0232.42007 [6] Vladimirov, V. S., Equations of Mathematical Physics (1967), Nauka: Nauka Moscow, in Russian · Zbl 0223.35002 [7] Whitaker, S., Diffusion and dispersion in porous media, AIChE J., 13, 420-427 (1967) [8] Yosida, K., Functional Analysis (1965), Springer-Verlag · Zbl 0126.11504 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.