On the connection of the classical and quantum mechanical completeness of a potential at infinity on complete Riemannian manifolds
- I. M. Oleinik
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Translated from Matematicheskie Zametki, Vol. 55, No. 4, pp. 65–73, April, 1994.
The author thanks M. A. Shubin for posing the problem, A. A. Shkalikov for useful discussions and remarks, and the referee for useful remarks.
- D. B. Sears, “Note on uniqueness of Green functions,”Canad. Journ. Math.,2, 314–325 (1950).
- B. M. Levitan, “On one theorem by Titchmarsh and Sears,”Uspekhi Mat. Nauk,16, No. 4, 175–178 (1961).
- R. S. Ismagilov, “On self-adjointness conditions for high order differential operators,”Dokl. Akad. Nauk SSSR,142, No. 6, 1239–1242 (1962).
- M. G. Gimadislamov, “Sufficient conditions for the coincidence of minimal and maximal partial differential operators and for the discreteness of their spectra,”Mat. Zametki,4, No. 3, 301–313 (1968).
- F. S. Rofe-Beketov, “Self-adjointness conditions for the Schrödinger operator,”Mat. Zametki,8, No. 6, 741–751 (1970).
- P. Chernoff, “Essential self-adjointness of powers of generators of hyperbolic equations,”J. Func. Anal.,12, No. 3, 401–414 (1973). CrossRef
- R. Strichardz, “Analysis of the Laplacian on the complete Riemannian manifolds,”J. Func. Anal.,52, No. 1, 48–79 (1983). CrossRef
- M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. 2.Fourier Analysis.SelfAdjointness [Russian translation], Mir, Moscow (1978).
- F. A. Berezin and M. A. Shubin,The Schrödinger Equation, Izdat. Moskov. Univ., Moscow (1983).
- M. R. Gaffney, “A special Stoke's theorem for complete Riemannian manifolds,”Ann. Math.,60, No. 1, 140–145 (1954).
- B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko,Modern Geometry. Methods and Applications, Nauka, Moscow (1986).
- I. Chavel,Eigenvalues in Riemannian Geometry, Academic Press, New York (1984).
- On the connection of the classical and quantum mechanical completeness of a potential at infinity on complete Riemannian manifolds
Volume 55, Issue 4 , pp 380-386
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- I. M. Oleinik (1)
- Author Affiliations
- 1. Moscow State University, USSR