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Local radial Phragmén-Lindelöf estimates for plurisubharmonic functions on analytic varieties


Authors: Rüdiger W. Braun, Reinhold Meise and B. A. Taylor
Journal: Proc. Amer. Math. Soc. 131 (2003), 2423-2433
MSC (2000): Primary 32U05, 32U15
DOI: https://doi.org/10.1090/S0002-9939-02-06764-3
Published electronically: November 13, 2002
MathSciNet review: 1974640
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Abstract: We give a sufficient condition for a local radial Phragmén-Lindelöf principle on analytic varieties. This condition is expressed in terms of existence of hyperbolic directions.


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  • 1. Andreotti, A., Nacinovich, M., Analytic convexity and the principle of Phragmén-Lindelöf, Quaderni della Scuola Normale de Pisa (1980). MR 83h:32018
  • 2. Bainbridge, D., Phragmén-Lindelöf estimates for plurisubharmonic functions of linear growth, Thesis, Ann Arbor 1998.
  • 3. Boiti, C., Nacinovich, M., The overdetermined Cauchy problem, Ann. Inst. Fourier (Grenoble) 47 (1997), 155-199. MR 98a:35095
  • 4. Braun, R.W., Hörmander's Phragmén-Lindelöf principle and irreducible singularities of codimension $1$, Boll. Un. Mat. Ital. 6 - A (1992), 339-348. MR 94b:35012
  • 5. Braun, R.W., Meise, R., Taylor, B.A., A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties, Ann. Polon. Math. LXXII (1999), 159-179. MR 2001b:32068
  • 6. Braun, R.W., Meise, R., Taylor, B.A., Algebraic varieties on which the classical Phragmén-Lindelöf estimates hold for plurisubharmonic functions, Math. Z. 232 (1999), 103-135. MR 2001d:32048
  • 7. Braun, R.W., Meise, R., Taylor, B.A., An example concerning the local radial Phragmén-Lindelöf condition, to appear in Recent Progress in Functional Analysis, Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, K. D. Bierstedt, J. Bonet, M. Maestre, J. Schmets (Eds.), North-Holland Math. Studies.
  • 8. Braun, R.W., Meise, R., Taylor, B.A., The geometry of analytic varieties satisfying the local Phragmén-Lindelöf condition and a geometric characterization of partial differential operators that are surjective on $\mathcal{A}(\mathbb{R} ^4)$, manuscript.
  • 9. Braun, R.W., Meise, R., Vogt, D., Characterization of the linear partial differential operators with constant coefficients which are surjective on non-quasianalytic classes of Roumieu type on $\mathbb{R} ^N$, Math. Nachr. 168 (1994), 19-54. MR 95g:35004
  • 10. Chirka, E. M., Complex Analytic Sets, Kluwer, Dordrecht, 1989. MR 92b:32016
  • 11. Franken, U., Meise, R., Extension and lacunas of solutions of linear partial differential equations, Ann. Inst. Fourier (Grenoble) 46 (1996), 154-161. MR 97h:35005
  • 12. Hörmander, L., On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-183. MR 49:817
  • 13. Kaneko, A., On Hartogs type continuation theorem for regular solutions of linear differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sect. IA 35 (1988), 1-26. MR 89m:35043
  • 14. Meise, R., Taylor, B.A., Phragmén-Lindelöf conditions for graph varieties, Result. Math. 36 (1999), 121-148. MR 2000j:32057
  • 15. Meise, R., Taylor, B.A., Vogt, D., Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse, Ann. Inst. Fourier (Grenoble) 40 (1990), 619-655. MR 92e:46083
  • 16. Meise, R., Taylor, B.A., Vogt, D., Extremal plurisubharmonic functions of linear growth on algebraic varieties, Math. Z. 219 (1995), 515-537. MR 96j:32019
  • 17. Meise, R., Taylor, B.A., Vogt, D., Phragmén-Lindelöf principles on algebraic varieties, J. Amer. Math. Soc. 11 (1998), 1-39. MR 98j:32007
  • 18. Momm, S., On the dependence of analytic solutions of partial differential equations on the right hand side, Trans. Amer. Math. Soc. 345 (1994), 729-752. MR 95a:46036
  • 19. Nevanlinna, R., Eindeutige analytische Funktionen, Springer, Berlin, Heidelberg, New York 1974. MR 49:9165
  • 20. Palamodov, V.I., A criterion for splitness of differential complexes with constant coefficients, in Geometrical and Algebraical Aspects in Several Complex Variables, C.A. Berenstein and D.C. Struppa (Eds.), Edit El (1991), pp. 265-290. MR 94d:58137
  • 21. Sibony, N., Wong, P., Some results on global analytic sets, Séminaire Lelong-Skoda (Analyse), Springer Lecture Notes, Vol. 822 (1978-79), 221-237. MR 82h:32017
  • 22. Siciak, J., Extremal plurisubharmonic functions and capacities in $\mathbb{C} ^n$, Sophia Kokyuroku in Mathematics 14, Tokyo 1982.
  • 23. Whitney, H., Complex Analytic Varieties. Addison-Wesley, Reading, Mass., 1972. MR 52:8473
  • 24. Zampieri, G., An application of the fundamental principle of Ehrenpreis to the existence of global solutions of linear partial differential equations, Boll. Un. Mat. Ital. 6 (1986), 361-392. MR 82m:35018b

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Additional Information

Rüdiger W. Braun
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
Email: Ruediger.Braun@uni-duesseldorf.de

Reinhold Meise
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
Email: meise@cs.uni-duesseldorf.de

B. A. Taylor
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: taylor@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06764-3
Received by editor(s): October 2, 2000
Received by editor(s) in revised form: March 11, 2002
Published electronically: November 13, 2002
Additional Notes: The authors gratefully acknowledge support of DAAD under the program “Projektbezogene Förderung des Wissenschaftleraustauschs mit den USA in Zusammenarbeit mit der National Science Foundation”
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society

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