Transition operators, groups, norms, and spectral radii

Pacific Journal of Mathematics

Volumn 180, Issue 2, 1997, Pages 333-367

  Saloff Coste, Laurent ^a   Woess, Wolfgang ^b  

^a CNRS   (France)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005409329     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1997.180.333     Document Type: Article

References (24)

1. G. Andrews, The theory of partitions, Addison-Wesley, 1976.
2. C. Berg and J.P.R. Christensen, On the relation between amenability of locally compact groups and the norms of convolution operators, Math. Ann., 208 (1974), 149-153.
3. _, Sur la norme des opérateurs de convolution, Inv. Math., 23 (1974), 173-178.
4. D.I. Cartwright and W. Młotkowski, Harmonic analysis for groups acting on triangle buildings, J. Austral. Math. Soc., 56 (1994), 345-383.
5. 2 groups, Ann. Inst. Fourier, (Grenoble), 44 (1993), 213-248.
6. D.I. Cartwright and P.M. Soardi, Harmonic analysis on the free product of two cyclic groups, J. Funct. Anal., 65 (1986), 163-180.
7. A. Figà-Talamanca and M.A. Picardello, Harmonic analysis on free groups, Lecture Notes in Pure and Appl. Math., 87, Marcel Dekker, New York, 1993.
8. J. Goldman and G.C. Rota, The number of subspaces of a vector space, in Recent progress in combinatorics, W. Tutte (ed.), Academic Press, (1969), 75-83.
9. P. de la Harpe, G. Robertson and A. Valette, On the spectrum of the sum of generators for a finitely generated group, Israel J. Math., 81 (1993), 65-96.
10. E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, I, Springer, Berlin-Heidelberg-New York, 1963.
11. A. Mantero and A. Zappa, Spherical functions and spectrum of the Laplacian operators on buildings of rank 2, Boll. Un. Mat. Ital., 8-B (1994), 419-475.
12. B. Mohar and W. Woess, A survey on spectra of infinite graphs, Bull. London Math. Soc., 21 (1989), 209-234.
13. C. Nebbia, On the amenability and the Kunze-Stein property for groups acting on a tree, Pacific J. Math., 135 (1988), 371-380.
14. M. Ronan, Lectures on Buildings, Academic Press, New York, 1989.
15. L. Saloff-Coste and W. Woess, Computing norms of group-invariant transition operators, Comb. Prob. Comp., 5 (1996), 161-178.
16. M. Salvatori, On the norm of group invariant transition operators on graphs, J. Theoret. Prob., 5 (1992), 563-576.
17. H. Schaefer, Topological vector spaces, 3rd printing, Springer, New York, 1971.
18. E. Seneta, Non-negative matrices and Markov chains, Springer Series in Statistics, 2nd ed., Springer, New-York, 1973.
19. J-P. Serre, Cours d'arithmétique, Presses Universitaires de France, 1970.
20. P. Soardi and W. Woess, Amenability, unimodularity, and the spectral radius of random walks on infinite graphs, Math. Zeit., 205 (1990), 471-486.
21. E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean spaces, Princeton University Press, 1971.
22. D. Vere-Jones, Ergodic properties of nonnegative matrices-I, Pacific J. Math., 22 (1967), 361-386.
23. _, Ergodic properties of nonnegative matrices-II, Pacific J. Math., 26 (1968), 601-620.
24. W. Woess, A local limit theorem for random walks on certain discrete groups, in: Probability measures on groups, Lect. Notes in Math., 928, Springer, (1982), 468-477.