Integral representations for harmonic and biharmonic functions in the unit ball (in Russian)

Author O. E. Yaremko
yaremki@mail.ru
ѕензенский государственный университет

Abstract In the paper an analytical solution of the analytic continuation problem in the unit N-dimensional ball by its values on the inner sphere is found. A generalization of the classical Poisson formula is obtained. A solution of the similar analytic continuation problem for certain known operator expressions of a given potential on the inner sphere is obtained. A new result of the moment problem making a connection between the moment problem on a segment and on the half-axis is found.
Keywords extension problem; Poisson formula; moment problems; biharmonic function; harmonic function; unit ball
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Pages 67-73
Volume 39
Issue 1
Year 2013
Journal Matematychni Studii
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