Publications of

Charles N. Delzell

Books, and articles in refereed journals and refereed conf.\ proceedings:

1. A finiteness theorem for open semialgebraic sets, with applications to Hilbert's 17th problem,
in Ordered Fields and Real Algebraic Geometry,
D.W. Dubois and T. Recio, eds.  Contemporary Math., Vol. 8 (1982),
Amer. Math. Soc., pp. 79-97.
Zbl. 495 (1983), 14013. MR83h:12033.

2. Case distinctions are necessary for representing polynomials as sums of squares,
in Proc. Herbrand Symp., Logic Coll. 1981,
Stud. Logic Found. Math. 107,
J. Stern, ed.  North Holland, 1982, pp. 87-103.
Zbl. 502 (1983), 03032. MR86i:11015.

3. Continuous sums of squares of forms,
in L.E.J. Brouwer Centenary Symp.,
Stud. Logic Found. Math. 110,
A.S. Troelstra and D. van Dalen, eds.
North Holland, 1982, pp. 65-75.
Zbl. 527 (1984), 10016.  MR85g:03086.

 4. A continuous, constructive solution to Hilbert's 17th problem,
Invent. math. 76(3) (1984), 365-84.
Zbl. 547 (1985), 12017. MR86e:12003.
Also reviewed by I. Stewart,
The power of positive thinking, Nature 315 (13 June 1985), 539;
and by Math. Magazine 59(1) (Feb. 1986), 55.

5. Piecewise-rational retractions onto closed, convex semi-algebraic sets with interior--synopsis,
Rocky Mountain J. Math. 14(4) (Fall 1984), 943-6.
Zbl. 571 (1986), 14014. MR86f:12009.

6. Analytic right-inverses for quadratic forms over number fields,
Bull. London Math. Soc. 17(5) (1985), 449-52.
Zbl. 595 (1987), 10014.  MR87b:11029.

7. Note on quantifier prefixes over diophantine equations,
Zeitschr. math. Logik Grundlagen Math. (replaced by Math. Logic Quarterly) 32(5) (1986), 395-7.
Zbl. 583, 03004.  MR88e:03062.

8. Continuous Pythagoras numbers for rational quadratic forms,
J. Number Theory26(3) (1987), 257-73.
Zbl.626 (1988), 10019.  MR88g:11017.
Computer & Info. Sys. Abst. 36(3), #88-04305C.

9. Correction to ``Note on quantifier prefixes over diophantine equations,''
Zeitschr. math. Logik Grundlagen Math. 34(3) (1988), 283-6.
Zbl.627, 03003.  MR89b:03072.

10. On the Pierce-Birkhoff conjecture over ordered fields,
Rocky Mountain J. Math. 19(3) (Summer 1989), 651-68.
Zbl. 715, 14047.  MR91b:14073.

11. A new rational and continuous solution for the Hilbert's 17th problem,
Extracta Mathematicae 7(1) (1992), 59-64
(with L. Gonzalez-Vega and H. Lombardi).

12. A continuous and rational solution to Hilbert's 17th problem, and several cases of the Positivstellensatz,
in Computational Algebraic Geometry, F. Eyssette, A. Galligo, eds.
Progress in Math., Vol. 109, Birkhäuser (1993), 61-75
(with L. Gonzalez-Vega and H. Lombardi).
(A preprint of this was also published by
Departamento de Matematicas, Estadistica y Computacion, of the Universidad de Cantabria (Spain),
Num. 9 (Julio 1992), 1-14.)

13. Continuous sums of squares of rational functions,
Seminaire de Structures Algebriques Ordonees 1991-1992,
Num. 42 (Fevrier 1993), F. Delon, M.A. Dickmann, D. Gondard, eds.,
Equipe de Logique Mathematique, Prepublications, Univ. Paris VII (CNRS), 1-6.

14. Continuous, piecewise-polynomial functions which solve Hilbert's 17th problem,
J. reine angew. Math. 440 (1993), 157--73.

15. Non-existence of analytically varying solutions to Hilbert's 17th problem,
in Recent Advances in Real Algebraic Geometry and Quadratic Forms,
Proc. RAGSQUAD Year, Berkeley, 1990-1991,
W. Jacob, et al, eds. Contemp. Math., Vol. 155, AMS (1994), 107-17.

16. A completely normal spectral space that is not a real spectrum,
J. Algebra169(1) (Oct. 1, 1994), 71-7 (with J. Madden).

17. Lattice-ordered rings and semialgebraic geometry: I,
in Real Analytic and Algebraic Geometry (Trento, 1992),
F. Broglia, et al, eds. , de Gruyter (1995), 103-29 (with J. Madden).

18. Impossibility of C-infinity variation or formal power series variation
in solutions to Hilbert's 17th problem, J. Algebra 275 (2004), 233-49.

B. Long article:

Kreisel's unwinding of Artin's proof,
in Kreiseliana: About and Around Georg Kreisel,
P. Odifreddi, ed., A K Peters, 1996, 113-246.
CMP 1 435 764, MR97m:01097.

C. Books:

1. Real algebraic geometry and ordered structures.
Papers from the special semester (RAGOS) and AMS Special Session
on Real Algebraic Geometry and Ordered Algebraic Structures
held at Louisiana State University, Baton Rouge, LA, January-May and April 17-21, 1996.
Edited by Charles N. Delzell and James J. Madden.
Contemp. Math., 253. AMS, Providence, RI, 2000. xxviii+287 pp. ISBN: 0-8218-0804-4.

2. Positive Polynomials:  From Hilbert's 17th Problem to Real Algebraic Geometry,
by Alexander Prestel and Charles N. Delzell,
Springer Monographs in Mathematics, 2001.  267 pp.
MR 2002k:13044.
Click here for a list of Errata and Updates for this book.

D. Abstracts:

(Under construction.)

Last updated September 18, 2005.

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