Green functions and spectra on free products of cyclic groups

K. Aomoto; Y. Kato

Annales de l'institut Fourier (1988)

  • Volume: 38, Issue: 1, page 59-85
  • ISSN: 0373-0956

Abstract

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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 argument.

How to cite

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Aomoto, K., and Kato, Y.. "Green functions and spectra on free products of cyclic groups." Annales de l'institut Fourier 38.1 (1988): 59-85. <http://eudml.org/doc/74794>.

@article{Aomoto1988,
abstract = {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 argument.},
author = {Aomoto, K., Kato, Y.},
journal = {Annales de l'institut Fourier},
keywords = {Green functions of a stochastic operator on a free product of cyclic groups; Morse theoretic arguments},
language = {eng},
number = {1},
pages = {59-85},
publisher = {Association des Annales de l'Institut Fourier},
title = {Green functions and spectra on free products of cyclic groups},
url = {http://eudml.org/doc/74794},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Aomoto, K.
AU - Kato, Y.
TI - Green functions and spectra on free products of cyclic groups
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 1
SP - 59
EP - 85
AB - 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 argument.
LA - eng
KW - Green functions of a stochastic operator on a free product of cyclic groups; Morse theoretic arguments
UR - http://eudml.org/doc/74794
ER -

References

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  1. [A1] K. AOMOTO, Spectral theory on a free group and algebraic curves, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 31 (1985), 297-317. Zbl0583.60068MR86m:58127
  2. [A2] K. AOMOTO, A formula of eigen-function expansions. Case of asymptotic trees, Proc. Japan Acad. Ser. A Math. Sci., 61 (1985), 11-14. Zbl0619.60007MR86m:22009
  3. [C] D.I. CARTWRIGHT & P. M. SOARDI, Random walks on free products, quotients and amalgams, Nagoya Math. J., 102 (1986), 163-180. Zbl0592.60052MR88i:60120a
  4. [F1] A. FIGÀ-TALAMANCA & M.A. PICARDELLO, Harmonic analysis on free groups, Lecture Notes in Pure and Appl. Math. 87, Dekker, New York, 1983. Zbl0536.43001MR85j:43001
  5. (F2) U. FULTON, Introduction to intersection theory in algebraic geometry, Regional Conf. in Math. 54, Amer. Math. Soc., Providence, 1983. Zbl0913.14001
  6. [H1] W.V.D. HODGE & D. PEDOE, Methods of algebraic geometry, Cambridge Univ. Press, London, 1951. 
  7. [H2] M. HASHIZUME, Canonical representations and Fock representations of free groups, preprint, 1984. 
  8. [I1] A. IOZZI & M.A. PICARDELLO, Spherical functions on symmetric graphs, Lecture Notes in Math. 992, Springer, Berlin-New York, 1982. Zbl0535.43005
  9. [I2] A. IOZZI & M.A. PICARDELLO, Graphs and convolution operators, Topics in Modern Harmonic Analysis, Turin, Milan, 1982. Zbl0537.43006
  10. [K] Ts. KAJIWARA, On irreducible decompositions of the regular representations of free groups, Boll. Un. Mat. Ital. A, 4 (1985), 425-431. Zbl0586.22004MR87i:22017
  11. [M1] A.M. MANTERO & A. ZAPPA, The Poisson transform and representations of a free group, J. Funct. Anal., 51 (1983), 373-399. Zbl0532.43006MR85b:22010
  12. [M2] J. MILNOR, Singular points of complex hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, Princeton, 1968. Zbl0184.48405MR39 #969
  13. [P] M. PICARDELLO & W. WOESS, Random walks on amalgams, Monatsh. Math., 100 (1985), 21-33. Zbl0564.60069MR87d:60066
  14. [S1] T. STEGER, Harmonic analysis for an anisotropic random walk on a homogeneous tree, thesis, Washington Univ., St. Louis, 1985. 
  15. [S2] G. SZEGÖ, Orthogonal polynomials, Amer. Math. Sc. Collq. 23, Amer. Math. Soc., Providence, 1939. Zbl0023.21505JFM65.0278.03
  16. [T] M. TODA, Theory of non-linear lattices, Ser. Solid-State Sci. 20, Springer, Berlin-New York, 1981. Zbl0465.70014MR82k:58052b

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