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Asymptotic Mean Value Properties of Meta- and Panharmonic Functions

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We study asymptotic mean value properties, their converse, and some related results for solutions (metaharmonic functions) to the m-dimensional Helmholtz equation and solutions (panharmonic functions) to the modified m-dimensional Helmholtz equation. Some of these properties have no analogues for harmonic functions.

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Authors and Affiliations

  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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Translated from Problemy Matematicheskogo Analiza 112, 2021, pp. 85-88.

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Kuznetsov, N. Asymptotic Mean Value Properties of Meta- and Panharmonic Functions. J Math Sci 259, 205–209 (2021). https://doi.org/10.1007/s10958-021-05611-z

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