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Decomposition of the invariant Laplacian in the complex ball
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We, in this note, decompose the invariant Laplacian of the unit complex ball of $\mathbb{C}^n$ by the radial part and tangential part as $$ \widetilde{\Delta}= \widetilde{\Delta}_{rad}+\widetilde{\Delta}_{tan}.$$ We give several properties and interpretations involved with this decomposition.
Abstract
We, in this note, decompose the invariant Laplacian of the unit complex ball of $\mathbb{C}^n$ by the radial part and tangential part as $$ \widetilde{\Delta}= \widetilde{\Delta}_{rad}+\widetilde{\Delta}_{tan}.$$ We give several properties and interpretations involved with this decomposition.
참고문헌 (4)
- E. G. Kwon, "Decomposition of the Laplacian and pluriharmonic Bloch functions", Filomat, 31(1), pp.97~102 (2017)
- 권언근, "On M-subharmonicity in the ball", 대한수학회논문집, 28(3), pp.511~516 (2013), 대한수학회
- W. Rudin, "Function Theory in the Unit Ball of Cn" (1980), Springer-Verlag
- M. Stoll, "Invariant Potential Theory in the Unit Ball of Cn" (1994), Cambridge University Press
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