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Beurling-Nevanlinna inequality for subfunctions of the stationary Schrödinger operator
Author:
Alexander Kheyfits
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2943-2950
MSC (2000):
Primary 31A05, 30C80, 35J10
Posted:
April 11, 2006
MathSciNet review:
2231618
Full-text PDF Free Access
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Additional Information
Abstract: The classical Beurling-Nevanlinna upper bound for subharmonic functions is extended to subsolutions of the stationary Schrödinger equation.
References
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Baernstein II, A. and Taylor, B. A., Spherical rearrangements, subharmonic functions, and
 functions in  space. Duke Math. J. 43(1976), 245-268. MR 0402083 (53:5906)
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Beurling, A., Études sur un problème de majoration. Thèse, Uppsala, 1933.
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Bonic, R. A., Hajian, G. V., Cranford, E., and Krantz, S., Freshman Calculus. D. C. Heath and Co. Lexington, MA, 1971.
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Hartman, P., Ordinary Differential Equations. John Wiley & Sons, New York - London - Sydney, 1964. MR 0171038 (30:1270)
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Hayman, W. K., Subharmonic Functions. Vol. 2. Academic Press, London - San Diego - New York - Berkeley - Boston - Sydney - Tokyo - Toronto, 1989. MR 1049148 (91f:31001)
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Hörmander, L. Notions of Convexity. Birkhäuser, Boston - Basel - Berlin, 1994. MR 1301332 (95k:00002)
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Kheyfits, A., The Riesz-Herglotz formula for generalized harmonic functions and their boundary behavior. Soviet Math. Dokl. 44(1992), 688-691. MR 1153552
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Levin, B. Ya. and Kheyfits, A., Asymptotic behavior of subfunctions of the Schrödinger operator in an
 dimensional cone. Soviet Math. Dokl. 38(1989), 109-112. MR 0968495 (91h:35099)
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Levin, B. Ya. and Kheyfits, A., Asymptotic behavior of subfunctions of the stationary Schrödinger operator. Preprint, http://arXiv/abs/math/021132896, 2002, 96 pp.
- 10.
Nevanlinna, R., Über eine Minimumaufgabe in der Theorie der konformen Abbildung. Ges. Wiss. Göttingen, Math. Phys. Kl. 37(1933), 103-115.
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Additional Information
Alexander Kheyfits
Affiliation:
Graduate School and Bronx Community College of The City University of New York, Bronx, New York 10453
Email:
akheyfits@gc.cuny.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08333-X
PII:
S 0002-9939(06)08333-X
Keywords:
Beurling-Nevanlinna inequality,
subharmonic functions associated with the stationary Schr\"{o}dinger operator
Received by editor(s):
May 19, 2004
Received by editor(s) in revised form:
April 26, 2005
Posted:
April 11, 2006
Dedicated:
To Iossif V. Ostrovskii on the occasion of his 70th Anniversary
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2006 by Alexander I. Kheyfits
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