Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Remarks on the local Hopf's lemma

Author: Vladimir Shklover
Journal: Proc. Amer. Math. Soc. 124 (1996), 2711-2716
MSC (1991): Primary 30B40; Secondary 30C20, 30D50
MathSciNet review: 1327043
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper deals with the problem of extending the recent work of M.S.Baouendi and L.P.Rothschild concerning harmonic functions vanishing to infinite order in the normal direction in balls and half-spaces. Contrary to what one expects, we show that the B.-R. result extends neither to arbitrary domains nor to cases when the normal is replaced by a curve transversal to the boundary. The exact criterion when the result holds in $\mathbf {R}^2$ is given.

References [Enhancements On Off] (What's this?)

  • [1] M.S.Baouendi and L.P.Rothschild, A local Hopf lemma and unique continuation for harmonic functions, Duke Math.J. 71, International Mathematics Research Notices 8 (1993), 245-251. MR 94i:31008
  • [2] P.J.Davis, The Schwarz Function and its Applications, The Carus Mathematical Monographs, MAA, 1974. MR 53:11031
  • [3] D.Khavinson, On reflection of harmonic functions in surfaces of revolution, Complex Variables 17 (1991), 7--14. MR 92j:31005
  • [4] B.F.Logan,Jr., Properties of high-pass signals, Dissertation presented to the Electrical Engineering Faculty of Columbia University, New York, 1965.
  • [5] H.S.Shapiro, Functions with a spectral gap, Bull.A.M.S. 79 (1973), 355--360. MR 49:7696
  • [6] H.S.Shapiro, Notes on a Theorem of Baouendi and Rothschild, TRITA-MAT-1994-0022, Royal Inst. of Tech., Stockholm, Sweden. CMP 95:17

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30B40, 30C20, 30D50

Retrieve articles in all journals with MSC (1991): 30B40, 30C20, 30D50

Additional Information

Vladimir Shklover
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742

Keywords: Harmonic functions, Hopf's lemma, analytic continuation
Received by editor(s): July 6, 1994
Received by editor(s) in revised form: February 28, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society