Elliptic operators on infinite graphs

Analysis, Geometry and Topology of Elliptic Operators

Volumn , Issue , 2006, Pages 353-368

  Dodziuk, Józef ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; GROUND STATE; PARTIAL DIFFERENTIAL EQUATIONS; TOPOLOGY;

CHEEGER; DIFFERENTIAL GEOMETRY; ELLIPTIC OPERATOR; INFINITE GRAPH; SEMI-GROUP; SPECTRAL THEORY;

GEOMETRY;

EID: 84992236533     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1142/9789812773609_0013     Document Type: Conference Paper

References (13)

1. R. BROOKS. The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv. 56 #4 (1981), 581-598.
2. P. BUSER. A note on the isoperimetric constant. Ann. Sci. École Norm. Sup. 15 (1982), 213-230.
3. J. CHEEGER. A lower bound for the smallest eigenvalue of the Laplacian. In: Problems in Analysis (Papers dedicated to Salomon Bochner, 1969), R. C. GUNNING, ed., 195-199. Princeton: Princeton University Press, 1970.
4. Y. COLIN DE VERDIÈRE. Spectres de graphes, Cours Spécialisés [Specialized Courses] 4. Paris: Société Mathématique de France, 1998.
5. J. DODZIUK. Maximum principle for parabolic inequalities and the heat flow on open manifolds. Indiana Univ. Math. J. 32 #5 (1983), 703-716.
6. J. DODZIUK. Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Amer. Math. Soc. 284 (1984), 787-794.
7. J. DODZIUK & W. KENDALL. Combinatorial Laplacian and isoperimetric inequality. In: From local times to global geometry, control and physics, K. D. ELLWORTHY, ed., Pitman Res. Notes Math. Ser. 150, 68-74. Harlow: Longman Scientific & Technical, 1986.
8. J. DODZIUK & V. MATHAI. Kato's inequality and asymptotic spectral properties for discrete magnetic laplacians. In: Geometry of the Laplace Operator, J. JORGENSON & L. WALLING, eds., Contemporary Mathematics. Ubiquitous Heat Kernels, to appear.
9. A. LUBOTZKY. Discrete groups, expanding graphs and invariant measures, Progress in Mathematics 125. Basel: Birkhäuser Verlag, 1994. With an appendix by Jonathan D. Rogawski.
10. R. G. PINSKY. Positive harmonic functions and diffusion, Cambridge Studies in Advanced Mathematics 45. Cambridge: Cambridge University Press, 1995.
11. M. H. PROTTER & H. F. WEINBERGER. Maximum principles in differential equations. New York: Springer-Verlag, 1984. Corrected reprint of the 1967 original.
12. M. REED & B. SIMON. Methods of modern mathematical physics. II. Fourier analysis, self-adjointness. New York: Academic Press [Harcourt Brace Jo-vanovich Publishers], 1975.
13. D. SULLIVAN. Related aspects of positivity: λ-potential theory on manifolds, lowest eigenstates, Hausdorff geometry, renormalized Markoff processes⋯ In: Aspects of mathematics and its applications, J. A. BARROSO, ed., North-Holland Math. Library, 34, 747-779. Amsterdam: North-Holland, 1986.