On the pythagoras numbers of real analytic surfaces

Francesca Acquistapace; Fabrizio Broglia; José F. Fernando; Jesús M. Ruiz

Annales scientifiques de l'École Normale Supérieure (2005)

  • Volume: 38, Issue: 5, page 751-772
  • ISSN: 0012-9593

How to cite

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Acquistapace, Francesca, et al. "On the pythagoras numbers of real analytic surfaces." Annales scientifiques de l'École Normale Supérieure 38.5 (2005): 751-772. <http://eudml.org/doc/82673>.

@article{Acquistapace2005,
author = {Acquistapace, Francesca, Broglia, Fabrizio, Fernando, José F., Ruiz, Jesús M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Pythagoras number; analytic function; analytic function germ; meromorphic function; meromorphic function germ},
language = {eng},
number = {5},
pages = {751-772},
publisher = {Elsevier},
title = {On the pythagoras numbers of real analytic surfaces},
url = {http://eudml.org/doc/82673},
volume = {38},
year = {2005},
}

TY - JOUR
AU - Acquistapace, Francesca
AU - Broglia, Fabrizio
AU - Fernando, José F.
AU - Ruiz, Jesús M.
TI - On the pythagoras numbers of real analytic surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2005
PB - Elsevier
VL - 38
IS - 5
SP - 751
EP - 772
LA - eng
KW - Pythagoras number; analytic function; analytic function germ; meromorphic function; meromorphic function germ
UR - http://eudml.org/doc/82673
ER -

References

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  1. [1] Acquistapace F., Broglia F., Fernando J.F., Ruiz J.M., On the 17th Hilbert Problem for global analytic functions, Preprint RAAG 2004. 
  2. [2] Andradas C., Díaz-Cano A., Ruiz J.M., The Artin–Lang property for normal real analytic surfaces, J. reine angew. Math.556 (2003) 99-111. Zbl1037.32010MR1971140
  3. [3] Bochnak J., Coste M., Roy M.F., Real Algebraic Geometry, Ergeb. Math. Grenzgeb., vol. 36, Springer, Berlin, 1998. Zbl0912.14023MR1659509
  4. [4] Cartan H., Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France85 (1957) 77-99. Zbl0083.30502MR94830
  5. [5] Choi M.D., Dai Z.D., Lam T.Y., Reznick B., The Pythagoras number of some affine algebras and local algebras, J. reine angew. Math.336 (1982) 45-82. Zbl0499.12018MR671321
  6. [6] Coen S., Sul rango dei fasci coerenti, Boll. Univ. Mat. Ital.22 (1967) 373-383. Zbl0164.38202MR227467
  7. [7] Greenberg M.J., Lectures on Forms in Many Variables, W.A. Benjamin, New York, 1969. Zbl0185.08304MR241358
  8. [8] Gunning R., Rossi H., Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, NJ, 1965. Zbl0141.08601MR180696
  9. [9] Jaworski P., Positive definite analytic functions and vector bundles, Bull. Acad. Pol. Sci.30 (1982) 501-506. Zbl0554.32006MR718726
  10. [10] Jaworski P., About estimates on number of squares necessary to represent a positive-semidefinite analytic function, Arch. Math.58 (1992) 276-279. Zbl0723.14043MR1148203
  11. [11] de Jong T., Pfister G., Local Analytic Geometry, Basic Theory and Applications, Advanced Lectures in Mathematics, Vieweg, Braunschweig, 2000. Zbl0959.32011MR1760953
  12. [12] Lam T.Y., The Algebraic Theory of Quadratic Forms, Mathematics Lecture Notes Series, W.A. Benjamin, Massachusetts, 1973. Zbl0259.10019MR396410
  13. [13] Mahé L., Level and Pythagoras number of some geometric rings, Math. Z.204 (4) (1990) 615-629. Zbl0773.11024MR1062139
  14. [14] Mahé L., Théorème de Pfister pour les variétés et anneaux de Witt réduits, Invent. Math.85 (1) (1986) 53-72. Zbl0601.14019MR842048
  15. [15] Narasimhan R., Introduction to the Theory of Analytic Spaces, Lecture Notes in Math., vol. 25, Springer, Berlin, 1966. Zbl0168.06003MR217337
  16. [16] Pfister A., Quadratic Forms with Applications to Algebraic Geometry and Topology, London Math. Soc. Lecture Note Ser., vol. 217, Cambridge University Press, Cambridge, 1995. Zbl0847.11014MR1366652
  17. [17] Prestel A., Delzell C.N., Positive Polynomials, Monographs in Mathematics, Springer, Berlin, 2001. Zbl0987.13016MR1829790
  18. [18] Ruiz J.M., The Basic Theory of Power Series, Advanced Lectures in Mathematics, Vieweg, Braunschweig, 1993. MR1234937
  19. [19] Tougeron J.-C., Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb., vol. 71, Springer, Berlin, 1972. Zbl0251.58001MR440598

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