Ochakovskaya, O. A. Theorems on ball mean values for solutions of the Helmholtz equation on unbounded domains. (English. Russian original) Zbl 1246.35071 Izv. Math. 76, No. 2, 365-374 (2012); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 76, No. 2, 161-170 (2012). In this article, a geometric description of the set of solutions of the Helmholtz equation on unbounded domains is obtained. The author extends the spherical mean theorem for solutions of the Helmholtz equation for half-spaces. Reviewer: Andreas Kleefeld (Cottbus) Cited in 1 Document MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 43A90 Harmonic analysis and spherical functions 58C35 Integration on manifolds; measures on manifolds 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:Helmholtz equation; ball means; spherical means; eigenfunctions of the Laplace operator PDFBibTeX XMLCite \textit{O. A. Ochakovskaya}, Izv. Math. 76, No. 2, 365--374 (2012; Zbl 1246.35071); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 76, No. 2, 161--170 (2012) Full Text: DOI