Series expansion and reproducing kernels for hyperharmonic functions. (English) Zbl 0992.31004
Summary: First the authors show that any hyperbolically harmonic (hyperharmonic) function in the unit ball \(B\) in \(\mathbb{R}^n\) has a series expansion in hyperharmonic functions, and then they construct the kernel that reproduces hyperharmonic functions in some \(L^1(B)\) space. The authors show that the same kernel also reproduces harmonic functions in \(L^1(B)\).
Reviewer: S.K.Rangarajan (Bangalore)
MSC:
| 31B10 | Integral representations, integral operators, integral equations methods in higher dimensions |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 35C10 | Series solutions to PDEs |
References:
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