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Green functions and spectra on free products of cyclic groups. (English) Zbl 0639.60008
Green functions of a stochastic operator on a free product of cyclic groups are explicitly evaluated as algebraic functions. The spectra are investigated by Morse theoretic arguments.

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
20E05 Free nonabelian groups
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[1] K. AOMOTO, Spectral theory on a free group and algebraic curves, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 31 (1985), 297-317. · Zbl 0583.60068
[2] K. AOMOTO, A formula of eigen-function expansions. Case of asymptotic trees, Proc. Japan Acad. Ser. A Math. Sci., 61 (1985), 11-14. · Zbl 0619.60007
[3] D.I. CARTWRIGHT & P. M. SOARDI, Random walks on free products, quotients and amalgams, Nagoya Math. J., 102 (1986), 163-180. · Zbl 0592.60052
[4] A. FIGÀ-TALAMANCA & M.A. PICARDELLO, Harmonic analysis on free groups, Lecture Notes in Pure and Appl. Math. 87, Dekker, New York, 1983. · Zbl 0536.43001
[5] (F2) U. FULTON, Introduction to intersection theory in algebraic geometry, Regional Conf. in Math. 54, Amer. Math. Soc., Providence, 1983. · Zbl 0913.14001
[6] W.V.D. HODGE & D. PEDOE, Methods of algebraic geometry, Cambridge Univ. Press, London, 1951. · Zbl 0055.38705
[7] M. HASHIZUME, Canonical representations and Fock representations of free groups, preprint, 1984.
[8] A. IOZZI & M.A. PICARDELLO, Spherical functions on symmetric graphs, Lecture Notes in Math. 992, Springer, Berlin-New York, 1982. · Zbl 0535.43005
[9] A. IOZZI & M.A. PICARDELLO, Graphs and convolution operators, Topics in Modern Harmonic Analysis, Turin, Milan, 1982. · Zbl 0537.43006
[10] Ts. KAJIWARA, On irreducible decompositions of the regular representations of free groups, Boll. Un. Mat. Ital. A, 4 (1985), 425-431. · Zbl 0586.22004
[11] A.M. MANTERO & A. ZAPPA, The Poisson transform and representations of a free group, J. Funct. Anal., 51 (1983), 373-399. · Zbl 0532.43006
[12] J. MILNOR, Singular points of complex hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, Princeton, 1968. · Zbl 0184.48405
[13] M. PICARDELLO & W. WOESS, Random walks on amalgams, Monatsh. Math., 100 (1985), 21-33. · Zbl 0564.60069
[14] T. STEGER, Harmonic analysis for an anisotropic random walk on a homogeneous tree, thesis, Washington Univ., St. Louis, 1985.
[15] G. SZEGÖ, Orthogonal polynomials, Amer. Math. Sc. Collq. 23, Amer. Math. Soc., Providence, 1939. · Zbl 0023.21505
[16] M. TODA, Theory of non-linear lattices, Ser. Solid-State Sci. 20, Springer, Berlin-New York, 1981. · Zbl 0465.70014
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