TY - JOUR
T1 - Harmonic functions vanishing on a cone
AU - Mangoubi, Dan
AU - Weller Weiser, Adi
N1 - Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - Let Z be a quadratic harmonic cone in ℝ 3 . We consider the family H(Z) of all harmonic functions vanishing on Z. Is H(Z) finite or infinite dimensional? Some aspects of this question go back to as early as the 19th century. To the best of our knowledge, no nondegenerate quadratic harmonic cone exists for which the answer to this question is known. In this paper we study the right circular harmonic cone and give evidence that the family of harmonic functions vanishing on it is, maybe surprisingly, finite dimensional. We introduce an arithmetic method to handle this question which extends ideas of Holt and Ille and is reminiscent of Hensel’s Lemma.
AB - Let Z be a quadratic harmonic cone in ℝ 3 . We consider the family H(Z) of all harmonic functions vanishing on Z. Is H(Z) finite or infinite dimensional? Some aspects of this question go back to as early as the 19th century. To the best of our knowledge, no nondegenerate quadratic harmonic cone exists for which the answer to this question is known. In this paper we study the right circular harmonic cone and give evidence that the family of harmonic functions vanishing on it is, maybe surprisingly, finite dimensional. We introduce an arithmetic method to handle this question which extends ideas of Holt and Ille and is reminiscent of Hensel’s Lemma.
UR - http://www.scopus.com/inward/record.url?scp=85059697539&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1823-9
DO - 10.1007/s11856-018-1823-9
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AN - SCOPUS:85059697539
SN - 0021-2172
VL - 230
SP - 563
EP - 581
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -