Beurling-Nevanlinna inequality for subfunctions of the stationary Schrödinger operator
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- by Alexander Kheyfits PDF
- Proc. Amer. Math. Soc. 134 (2006), 2943-2950
Abstract:
The classical Beurling-Nevanlinna upper bound for subharmonic functions is extended to subsolutions of the stationary Schrödinger equation.References
- Albert Baernstein II and B. A. Taylor, Spherical rearrangements, subharmonic functions, and $^*$-functions in $n$-space, Duke Math. J. 43 (1976), no. 2, 245–268. MR 402083
- Beurling, A., Études sur un problème de majoration. Thèse, Uppsala, 1933.
- Bonic, R. A., Hajian, G. V., Cranford, E., and Krantz, S., Freshman Calculus. D. C. Heath and Co. Lexington, MA, 1971.
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148
- Lars Hörmander, Notions of convexity, Progress in Mathematics, vol. 127, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1301332
- A. I. Kheĭfits, The Riesz-Herglotz formula for generalized harmonic functions and their boundary behavior, Dokl. Akad. Nauk SSSR 321 (1991), no. 2, 263–265 (Russian); English transl., Soviet Math. Dokl. 44 (1992), no. 3, 688–691. MR 1153552
- B. Ya. Levin and A. I. Kheĭfits, Asymptotic behavior of subfunctions of the Schrödinger operator in an $n$-dimensional cone, Dokl. Akad. Nauk SSSR 301 (1988), no. 3, 540–543 (Russian); English transl., Soviet Math. Dokl. 38 (1989), no. 1, 109–112. MR 968495
- Levin, B. Ya. and Kheyfits, A., Asymptotic behavior of subfunctions of the stationary Schrödinger operator. Preprint, http://arXiv/abs/math/021132896, 2002, 96 pp.
- Nevanlinna, R., Über eine Minimumaufgabe in der Theorie der konformen Abbildung. Ges. Wiss. Göttingen, Math. Phys. Kl. 37(1933), 103-115.
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
- Received by editor(s): May 19, 2004
- Received by editor(s) in revised form: April 26, 2005
- Published electronically: April 11, 2006
- Communicated by: Juha M. Heinonen
- © Copyright 2006 by Alexander I. Kheyfits
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2943-2950
- MSC (2000): Primary 31A05, 30C80, 35J10
- DOI: https://doi.org/10.1090/S0002-9939-06-08333-X
- MathSciNet review: 2231618
Dedicated: To Iossif V. Ostrovskii on the occasion of his 70th Anniversary