Harmonic functions on locally finite networks

Results in Mathematics

Volumn 45, Issue 1-2, 2004, Pages

  von Below, Joachim ^a   Lubary, José A ^b  

^a UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

05C10; 05C50; 31C05; 35J05; eigenvalue problems; harmonic functions; Liouville spaces; Locally finite graphs and networks

Indexed keywords

EID: 65049086182     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322993     Document Type: Article

References (16)

1. 2-networks, Lin. Alg. Appl. 71 (1985) 309–325
2. J. von Below, Parabolic network equations, 3rd edition to appear
3. J. von Below, The index of a periodic graph, Results in Math. 25 (1994) 198–223
4. J. von Below, Can one hear the shape of a network? in: Partial Differential Equations on Multistructures, Lecture Notes in Pure and Applied Mathematics Vol. 219, Marcel Dekker Inc. New York, (2000) 19–36
5. J. von Below and J. A. Lubary, On the Laplacian on locally finite networks, in progress
6. N. L. Biggs, Algebraic graph theory. Cambridge Tracts Math. 67, Cambridge University Press, 1967
7. C. Cattaneo, The spectrum of the continuous Laplacian on a graph, Monatshefte für Mathematik 124 (1997) 215–235
8. L. Collatz, Spektren periodischer Graphen, Resultate der Mathematik 1 (1979) 42–53
9. D. M. Cvetcović, M. Doob, H. Sachs, Spectra of graphs. Academic Press New York, 1980
10. J. A. Lubary, Multiplicity of solutions of second order linear differential equations on networks, Lin. Alg. Appl. 274 (1998) 301–315
11. J. A. Lubary, Multiplicidad y valores propios no reales en problemas de contorno para ecuaciones diferenciales sobre redes, Doctoral Thesis UPC Barcelona, 2000
12. J. A. Lubary, On the geometric and algebraic multiplicities for eigenvalue problems on graphs, in: Partial Differential Equations on Multistructures, Lecture Notes in Pure and Applied Mathematics Vol. 219, Marcel Dekker Inc. New York, (2000) 135–146
13. B. Mohar and W. Woess, A survey on spectra of infinite graphs, Bull. London Math. Soc. 21 (1989) 209–234
14. e Série 111 (1987) 401–413
15. W. Woess, Random walks on infinite graphs and groups, Cambridge Univ. Press 138, 2000
16. R. J. Wilson, Introduction to graph theory, Oliver & Boyd Edinburgh, 1972