An extension of the theory of Fredholm determinants

David Ruelle

Publications Mathématiques de l'IHÉS (1990)

  • Volume: 72, page 175-193
  • ISSN: 0073-8301

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Ruelle, David. "An extension of the theory of Fredholm determinants." Publications Mathématiques de l'IHÉS 72 (1990): 175-193. <http://eudml.org/doc/104070>.

@article{Ruelle1990,
author = {Ruelle, David},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Fredholm's determinant theory; resolvent; quotient of an operator-valued entire function; integral operators},
language = {eng},
pages = {175-193},
publisher = {Institut des Hautes Études Scientifiques},
title = {An extension of the theory of Fredholm determinants},
url = {http://eudml.org/doc/104070},
volume = {72},
year = {1990},
}

TY - JOUR
AU - Ruelle, David
TI - An extension of the theory of Fredholm determinants
JO - Publications Mathématiques de l'IHÉS
PY - 1990
PB - Institut des Hautes Études Scientifiques
VL - 72
SP - 175
EP - 193
LA - eng
KW - Fredholm's determinant theory; resolvent; quotient of an operator-valued entire function; integral operators
UR - http://eudml.org/doc/104070
ER -

References

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  1. [1] V. BALADI and G. KELLER, Zeta functions and transfer operators for piecewise monotone transformations, Commun. Math. Phys., 127 (1990), 459-477. Zbl0703.58048MR91b:58196
  2. [2] R. BOWEN, Markov positions for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971), 377-397. Zbl0212.29103MR43 #8084
  3. [3] D. FRIED, The zeta functions of Ruelle and Selberg, I., Ann. Sci. E.N.S., 19 (1986), 491-517. Zbl0609.58033MR88k:58134
  4. [4] A. GROTHENDIECK, Produits tensoriels topologiques et espaces nucléaires, Memoirs of the Amer. Math. Soc., 16, Providence, RI, 1955. Zbl0064.35501MR17,763c
  5. [5] A. GROTHENDIECK, La théorie de Fredholm, Bull. Soc. Math. France, 84 (1956), 319-384. Zbl0073.10101MR19,558d
  6. [6] N. HAYDN, Meromorphic extension of the zeta function for Axiom A flows, Ergod. Th. and Dynam. Syst., 10 (1990), 347-360. Zbl0694.58035MR91g:58219
  7. [7] D. MAYER, On a ζ function related to the continued fraction transformation, Bull. Soc. Math. France, 104 (1976), 195-203. Zbl0328.58011MR54 #6210
  8. [8] R. D. NUSSBAUM, The radius of the essential spectrum, Duke Math. J., 37 (1970), 473-478. Zbl0216.41602MR41 #9028
  9. [9] M. POLLICOTT, A complex Ruelle-Perron-Frobenius theorem and two counterexamples, Ergod. Th. and Dynam. Syst., 4 (1984), 135-146. Zbl0575.47009MR88i:58097
  10. [10] F. RIESZ et B. SZ-NAGY, Leçons d'analyse fonctionnelle, 3e éd., Académie des Sciences de Hongrie, 1955. Zbl0064.35404MR16,837b
  11. [11] D. RUELLE, Zeta-functions for expanding maps and Anosov flows, Inventiones Math., 34 (1976), 231-242. Zbl0329.58014MR54 #8732
  12. [12] D. RUELLE, Thermodynamic Formalism, Encyclopedia of Math and its Appl., 5, Addison-Wesley, Reading, Massachussetts, 1978. Zbl0401.28016MR80g:82017
  13. [13] D. RUELLE, The thermodynamic formalism for expanding maps, Commun. Math. Phys., 125 (1989), 239-262. Zbl0702.58056MR91a:58149
  14. [14] Ia. G. SINAI, Construction of Markov partitions, Funkts. Analiz i ego Pril., 2, No. 3 (1968), 70-80. English translation: Functional Anal. Appl., 2 (1968), 245-253. Zbl0194.22602
  15. [15] F. TANGERMAN, Meromorphic continuation of Ruelle zeta functions, Boston University Thesis, 1986 (unpublished). 

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