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Spherical means and iterated Helmholtz operators. (Moyennes sphériques et opérateur de Helmholtz itéré.) (French) Zbl 0840.43002

Extending well known results valid for harmonic functions or more generally solutions for the Helmholtz equation, \(\Delta f + cf = 0\), the author gives a mean value formula for solutions of the iterated Helmholtz equation \((\Delta + c)^kf = 0\).

MSC:

43A07 Means on groups, semigroups, etc.; amenable groups
35J30 Higher-order elliptic equations
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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