operator;L-harmonic function;L-massive set;end;"/> operator;L-harmonic function;L-massive set;end;"/> BOUNDED SOLUTIONS FOR THE $SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS | Korea Science
JOURNAL BROWSE
Search
Advanced SearchSearch Tips
BOUNDED SOLUTIONS FOR THE $SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
BOUNDED SOLUTIONS FOR THE $SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS
Kim, Seok-Woo; Lee, Yong-Hah;
  PDF(new window)
 Abstract
Let M be a complete Riemannian manifold and L be a operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on the L-nonparabolic end, which vanish at the boundary of the end.
 Keywords
operator;L-harmonic function;L-massive set;end;
 Language
English
 Cited by
 References
1.
A. A. Grigor'yan, On the set of positive solutions of the Laplace-Beltrami equation on Riemannian manifolds of a special form, Izv. Vyssh. Uchebn. Zaved., Matematika (1987), no. 2, 30-37: English transl. Soviet Math. (Iz, VUZ) 31 (1987), no. 2, 48-60

2.
A. A. Grigor'yan, On Liouville theorems for harmonic functions with ?nite Dirichlet integral, (In Russian) Matem. Sbornik 132 (1987), no. 4, 496-516: English transl. Math. USSR Sbornik 60 (1988), no. 2, 485-504

3.
A. A. Grigor'yan, Dimensions of spaces of harmonic functions, Mat. Zametki 48 (1990), no. 5, 55-61; translation in Math. Notes 48 (1990), no. 5-6, 1114-1118

4.
A. A. Grigor'yan and W. Hansen, Liouville property for SchrAodinger operators, Math. Ann. 312 (1998), no. 4, 659-716 crossref(new window)

5.
S. W. Kim and Y. H. Lee, Generalized Liouville property for SchrAodinger operator on Riemannian manifolds, Math. Z. 238 (2001), no. 2, 355-387 crossref(new window)

6.
S. W. Kim and Y. H. Lee, Rough isometry and energy finite solutions for the SchrAodinger operator on Riemannian manifolds, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 4, 855-873

7.
P. Li and L-F. Tam, Positive harmonic functions on complete manifolds with nonnegative curvature outside a compact set, Ann. of Math. (2) 125 (1987), no. 1, 171-207 crossref(new window)

8.
P. Li and L-F. Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geom. 35 (1992), no. 2, 359-383 crossref(new window)

9.
C. J. Sung, L. F. Tam and J. Wang, Spaces of harmonic functions, J. London Math. Soc. (2) 61 (2000), no. 3, 789-806 crossref(new window)

10.
S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228 crossref(new window)