Eigenvalues of the discrete p-Laplacian for graphs

Ars Combinatoria

Volumn 67, Issue , 2003, Pages 283-302

  Amghibech, S ^a  

^a UNIVERSITÉ DE ROUEN   (France)

Author keywords

Dirichlet form; Eigenfunction; Eigenvalue; Graphs; Isoperimetric constant; Isoperimetric inequalities; p Laplacian; Trees

Indexed keywords

EID: 14944341947     PISSN: 03817032     EISSN: 28175204     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. 1, isoperimetric inequalities for graphs. and superconcentrators. J. Comb. Theory, Ser B, 38(8):73-R8, 1985.
2. [Amg97] S. Amghibech. Inégalités isopérimé triqucs pour les graphes. Potential Anal., 6(4):355-367, 1997.
3. [Amg98] S. Amghibech. The non-linear Wiener criterion for trees. preprint, 1998.
4. [BD58] A. Beurling and J. Deny. Espaces de Dirichlet. I: Le cas elementaire. Acta math., 99:203-224, 1958.
5. [CDS80] D. Cvetković, M. Doob, and H. Sachs. Spectra of graph. Theory and application. Academic press INC, New York, 1980.
6. [Che70] J. Cheeger. A lower bound for the smallest eigenvalue of the Laplacian. In Prob. Anal-ysis, Sympos. in Honor of Salomon Bochner, pages 195-199. Princeton Univ., 1970.
7. [Chu97] F. R. K. Chung. Spectral Graph Theory. Number 92 in CBMS. AMS Providence, 1997.
8. [CRS97] D. Cvetković, R. Rowlinson, and S. Simlć. Eigenspaces of Graphs, volume 66 of Encyclopedia of mathematics and its applications. Cambridge university press, 1997.
9. [Dav89] E. B. Davies. Heat kernels and spectral theory. Cambridge university press. Cambridge, 1989.
10. [DK88] J. Dodziuk and L. Karp. Spectral and function theory for combinatorial Laplacians. In Geometry of random motion, volume 73 of Contemp. Math., pages 23-40. Proc. AMS-IMS-SIAM, 1988.
11. [Dod84] J. Dodziuk. Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Amer. Math. Soc., 284:787-794, 1984.
12. [DS91] P. Diaconis and D. Stroock. Geometric bounds for eigenvalues of Murkov chiains. Ann. Appl. Probab., 1(1):36-61, 1991.
13. [DSC96a] P. Diaconis and L. Saloff-Coste. Logarithmic Snbolev inequalities tor finite Markov chains. Ann. Appl. Probab., 6(3):695-750, 1996.
14. [DSC96b] P. Diaconis and L. Saloff-Coste. Nash inequalities for finite Markov chains. J. Theor. Probab., 9(2):459-510, 1996.
15. [Gro93] L. Gross. Logarithmic Sobolev Inequalities and Contractivity Properties of Semigroups. In G. Dell'Antonio and U. Mosco, editors, Dirichlet forms, number 1563 in Lecture Notes in Mathematics, pages 54-88. Springer-Verlag. 1993.
16. [HS97] I. Holopainen and M. P. Soardi. A strong Liouville theorem for p-harmonic functions on graphs. Annals Academiae Scientiarum Finicae Mathematica, 22:205-226, 1997.
17. [Kai92] V. A. Kaimanovich. Dirichlet norms, capacities and generalized isoperimetric inequnlities for Markov operators. Potential Anal., 1(1):61-82, 1992.
18. [KY84] T. Kayano and M. Yamasaki. Boundary limit of discrete dirichlet potential. Hiroshima Math. J., 14:401-406, 1984.
19. p-2u = 0. Proc. Amer. Math. Soc., 109(1):157-164, 1990.
20. [Lin93] P. Lindqvist. On nonlinear Rayleigh quotients. Potential Anal., 2(3):193-218, 1993.
21. 2 spectrum for Markov chains and Markov processes: A generalization of Cheeger's inequality. Trans. Amer Math. Soc., 309(2):557-580, 1988.
22. [Lub94] A. Lubotzky. Discrete Groups, Expanding Graphs and Invariant Measures. volume 125. Birkhauser, 1994.
23. [NY76] T. Nakamura and M. Yanmsaki. Generalized extremal length of an infinite network. Hiroshima Math. J., 6:95- 111, 1976.
24. [NY77] T. Nakamura and M. Yamasaki. Minimal cut problems on an infinite network. Hiroshima Math. J., 7:597-603. 1977.
25. [PS51] G. Pólya and G. Szegö. Isoperimetric inequalities in mathematical physics Ann. Math. Studies, 27, 1951.
26. [SC97] L. Saloff-Coste. Lectures on finite Markov chians. In P. Bernard. editor. Lectures on probability theory and statistics, number 1665 in Lecture Notes in Mathematics. pages 301-413. Springer-Verlag, 1997.
27. [Yam77] M. Yamasaki. Parabolic and hyperbolic infinite networks. Hiroshima Math. J., 7:135-146, 1977.
28. [Yam86] M. Yamasaki. Ideal boundary limit of discrete Dirichlet functions. Hiroshima Math. J., 16:353-360, 1986.