# Green functions and spectra on free products of cyclic groups

Annales de l'institut Fourier (1988)

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

## Access Full Article

top## Abstract

top## How to cite

topAomoto, 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

top- [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
- [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
- [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
- [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
- (F2) U. FULTON, Introduction to intersection theory in algebraic geometry, Regional Conf. in Math. 54, Amer. Math. Soc., Providence, 1983. Zbl0913.14001
- [H1] W.V.D. HODGE & D. PEDOE, Methods of algebraic geometry, Cambridge Univ. Press, London, 1951.
- [H2] M. HASHIZUME, Canonical representations and Fock representations of free groups, preprint, 1984.
- [I1] A. IOZZI & M.A. PICARDELLO, Spherical functions on symmetric graphs, Lecture Notes in Math. 992, Springer, Berlin-New York, 1982. Zbl0535.43005
- [I2] A. IOZZI & M.A. PICARDELLO, Graphs and convolution operators, Topics in Modern Harmonic Analysis, Turin, Milan, 1982. Zbl0537.43006
- [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
- [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
- [M2] J. MILNOR, Singular points of complex hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, Princeton, 1968. Zbl0184.48405MR39 #969
- [P] M. PICARDELLO & W. WOESS, Random walks on amalgams, Monatsh. Math., 100 (1985), 21-33. Zbl0564.60069MR87d:60066
- [S1] T. STEGER, Harmonic analysis for an anisotropic random walk on a homogeneous tree, thesis, Washington Univ., St. Louis, 1985.
- [S2] G. SZEGÖ, Orthogonal polynomials, Amer. Math. Sc. Collq. 23, Amer. Math. Soc., Providence, 1939. Zbl0023.21505JFM65.0278.03
- [T] M. TODA, Theory of non-linear lattices, Ser. Solid-State Sci. 20, Springer, Berlin-New York, 1981. Zbl0465.70014MR82k:58052b

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.