References
Berg, C., Christensen, J.P.R.: On the relation between amenability of locally compact groups and the norms of convolution operators. Math. Ann.,208, 149–153 (1974)
Betori, W., Faraut, J., Pagliacci, M.: An inversion formula for the Radon transform on trees. Math. Z.201, 327–337 (1989)
Biggs, N.L., Mohar, B., Shawe-Taylor, J.: The spectral radius of infinite graphs. Bull. Lond. Math. Soc.20, 116–120 (1988)
Brooks, R.: The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv.56, 581–598 (1981)
Cartier, P.: Fonctions harmoniques sur un arbre. Symposia Math.9, 203–270 (1972)
Cartier, P.: Harmonic analysis on trees. Proc. Symp. Pure Math.9, 419–424 (1972)
Cohen, J.M.: Operator norms on free groups. Boll. Unione. Mat. Ital., VII. Ser., B1, 1055–1065 (1982)
Day, M.M.: Convolutions, means and spectra. Ill. J. Math.8, 100–111 (1964)
Dodziuk, J.: Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Am. Math. Soc.284, 787–794 (1984)
Dunwoody, M.J.: Cutting up graphs. Combinatorica2, 15–23 (1982)
Figà-Talamanca, A., Picadello, M.A.: Harmonic analysis on free groups. (Lect. Notes Pure Appl. Math., Vol. 87) New York: Dekker 1983
Freudenthal, H.: Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv.17, 1–38 (1944)
Gerl, P.: Random walks on graphs with a strong isoperimetric inequality. J. Theor. Probab.1, 171–188 (1988)
Gromov, M.: Infinite groups as geometric objects. Proc. Int. Congress Math., Warszawa 1983, pp. 385–392 (1984)
Guivarc'h, Y., Keane, M., Roynette, B.: Marches Aléatoires sur les Groupes de Lie. (Lect. Notes Math., Vol. 624) Berlin Heidelberg New York: Springer 1977
Halin, R.: Über unendliche Wege in Graphen. Math. Ann.157, 125–137 (1964)
Halin, R.: Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Semin. Univ. Hamb.39, 251–283 (1973)
Hewitt, E., Ross, K.A.: Abstract harmonic analysis, I. Berlin Heidelberg New York: Springer 1963
Ivanov, A.A.: Bounding the diameter of a distance-regular graph. Sov. Math. Dokl.28, 149–152 (1983)
Jung, H.A.: Connectivity in infinite graphs. In: L. Mirsky (ed.) Stud. Pure Math., pp. 137–143, New York London: Academic Press 1971
Jung, H.A.: A note on fragments of infinite graphs. Combinatorica1, 285–288 (1981)
Kesten, H.: Symmetric random walks on groups. Trans. Am. Math. Soc.92, 336–354 (1959)
Kesten, H.: Full Banach mean values on countable groups. Math. Scand.7, 146–156 (1959)
Leptin, H.: On locally compact groups with invariant means. Proc. Am. Math. Soc.19, 489–494 (1968)
Nebbia, C.: On the amenability and the Kunze-Stein property for groups acting on a tree. Pac. J. Math.135, 371–380 (1988)
Pier, J.P.: Amenable Locally Compact Groups. New York: Wiley 1984
Stallings, J.: Group Theory and Three-Dimensional Manifolds. New Haven: Yale University Press 1971
Trofimov, V.I.: Automorphism groups of graphs as topological objects. Math. Notes38, 717–720 (1985)
Woess, W.: Graphs and groups with tree-like properties. J. Comb. Theory, Ser. B47, 361–371 (1989)
Woess, W.: Amenable group actions on infinite graphs. Math. Ann.284, 251–265 (1989)
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Soardi, P.M., Woess, W. Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Math Z 205, 471–486 (1990). https://doi.org/10.1007/BF02571256
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DOI: https://doi.org/10.1007/BF02571256