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Mean Value Properties of Harmonic Functions and Related Topics (a Survey)

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Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes of functions.

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  1. Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, RAS, 61, V.O., Bol’shoy pr., St. Petersburg, 199178, Russia

    N. Kuznetsov

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  1. N. Kuznetsov
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Correspondence to N. Kuznetsov.

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To N. N. Uraltseva with deep respect

Translated from Problemy Matematicheskogo Analiza99, 2019, pp. 3-21.

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Kuznetsov, N. Mean Value Properties of Harmonic Functions and Related Topics (a Survey). J Math Sci 242, 177–199 (2019). https://doi.org/10.1007/s10958-019-04473-w

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