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math.AP2009
Malmheden's theorem revisited
M. Agranovsky, D. Khavinson, H. S. Shapiro
In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years la…
math.AP2009★ 3 cited
Range conditions for a spherical mean transform and global extension of solutions of Darboux equation
Mark Agranovsky, Linh V. Nguyen
The transform under study is defined by integration of functions over spheres centered on a sphere. Such transform is of interest due to its applications in analysis and (thermoaco…