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Stability in the Gromov-Shubin index theorem
Author(s):
Lih-chung
Wang
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1399-1405.
MSC (1991):
Primary 46E99, 58G10
MathSciNet review:
1363439
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Abstract:
We investigate the upper semicontinuity of the dimension of the solution space for an elliptic equation with conditions on a compact nowhere dense set.
References:
- [A-S]
- Atiyah, M. F., Singer, I. M.: The index of elliptic operators: III, Ann. of Math. (2) 87 (1968), 546-604. MR 38:5245
- [G-H]
- Griffiths, P., Harris, J.: Principles of algebraic geometry, Wiley, New York, 1978. MR 80b:14001
- [G-S]
- Gromov, M., Shubin, M.A.: The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets, Invent. Math. 117 (1994), 165-180. MR 95d:58121
- [H1]
- Hörmander, L.: The analysis of linear partial differential operators, Vol. I, Springer, Berlin, Heidelberg, and New York, 1983. MR 85g:35002a
- [H2]
- Hörmander, L.: The analysis of linear partial differential operators, Vol. III, Springer, Berlin, Heidelberg, and New York, 1985. MR 87d:35002a
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Additional Information:
Lih-chung
Wang
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, England
Address at time of publication:
Department of Mathematics, University of California, Riverside, California 92521
Email:
Lih-Chung.Wang@durham.ac.uk, lwang@math.ucr.edu
DOI:
10.1090/S0002-9939-97-03719-2
PII:
S 0002-9939(97)03719-2
Keywords:
Distribution,
elliptic operator,
Fredholm operator,
rigged divisor,
Sobolev space,
index,
Riemann-Roch theorem,
semicontinuity
Received by editor(s):
September 19, 1995
Received by editor(s) in revised form:
November 14, 1995
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
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