Papers

[2014b] Approximation on Nash sets with monomial singularities. Adv. Math. 262 (2014) 59-114. With E. Baro and J.F. Fernando.

[2014a] Finiteness problems on Nash manifolds and Nash sets. J. Eur. Math. Soc. 16 (2014) 537-570. With J.F. Fernando and J.M. Gamboa.

[2010] On the finiteness of Pythagoras numbers of real meromorphic functions. Bull. Soc. Math. France 138 (2010) 231-247 (MR 11c:14094; Zbl 1197.14060). With F. Acquistapace, F. Broglia and J.F. Fernando.

[2007] On the Pythagoras numbers of real analytic curves. Math. Z. 257 (2007) 13-21 (MR 08c:14075; Zbl 1126.14066). With F. Acquistapace, F. Broglia and J.F. Fernando.

[2006b] Sums of squares of linear forms. Math. Res. Lett. 13 (2006) 945-954 (MR 07m:11059; Zbl 1087.32003). With J.F. Fernando and C. Scheiderer.

[2006a] Sums of squares of linear forms: the quaternions approach. Preprint with J.F. Fernando and C. Scheiderer.(PDF)

[2005b] On the Pythagoras numbers of real analytic surfaces. Ann. Sc. École Norm. Sup. Paris 38 (2005) 751-772 (MR 07d:14104; Zbl 1087.32003). With F. Acquistapace, F. Broglia, J.F. Fernando.

[2005a] On the Pythagoras numbers of real analytic set germs. Bull. Soc. math. France 133 (2005) 349-362 (MR 06h:14065; Zbl 1095:14056). With J.F. Fernando.

[2004d] On the finiteness of Pythagoras numbers of real meromorphic functions. Preprint with F. Acquistapace, F. Broglia and J.F. Fernando. (PDF)

[2004c] On the Hilbert 17th Problem for global analytic functions.  Preprint with F. Acquistapace, F. Broglia and J.F. Fernando. (PDF)

[2004c] Determinación finita en anillos de series. Homenaje al Prof. Outerelo, Editorial Complutense (2004) 183-199. With J.F. Fernando. (PDF)

[2004b] Sums of squares in real rings. Trans. Amer. Math. Soc. 356 (2004) 2663-2684 (MR 05c:13028; Zbl 1080:14071). With J.F. Fernando and C. Scheiderer.

[2004a] Global problems on Nash functions. Rev. Mat. Complu. 17 (2004) 83-115 (MR 05c:14076; Zbl 1056.14081). With M. Coste and M. Shiota.  See the labyrinth of this paper.

[2003] The Artin-Lang property for normal real analytic surfaces. J. reine angew. Math. 556 (2003) 99-111 (MR 04f:14086; Zbl 1037.32010). With C. Andradas and A. Diaz-Cano.

[2002] Positive semidefinite germs on the cone. Pacific J. Math. 205 (2002) 109-118). With J.F. Fernando (MR 03f:14066; Zbl 1062.32008).

[2001] Uniform bounds on complexity and transfer of global properties of Nash functions. J. reine angew. Math. 536 (2001) 209-235 (MR 03c:14065; Zbl 981.14028). With M. Coste and M. Shiota.

[2000b] Problemas globales de las funciones de Nash. Homenaje al Prof. Arregui, Editorial Complutense (2000) 275-305 (MR 01i:14081; Zbl 986.14038).

[2000a] A separation bound for non-Hamiltonian differential equations with proper first integrals. J. Math. Phys. 41 (2000) 2922-2930 (MR 01a:34083; Zbl 979.34047). With F.G. Gascón and D. Peralta.

[1999b] Bounded meromorphic functions on compact real analytic sets. J. Pure Appl. Algebra 142 (1999) 1-11 (MR 00j:14094; Zbl 937.14040). With M.A. Abánades and N. Joglar-Prieto.

[1999a] Sums of two squares in analytic rings. Math. Z. 230 (1999) 317-328 (MR 00b:58068; Zbl 930.32007).

[1997] Real Algebraic and Analytic Geometry. Proceedings Segovia 1995. Rev. Matemática Complutense 1997. Coeditors: M.E. Alonso, C. Andradas, J.M. Gamboa, T. Recio.

[1996] Separation, factorization and finite sheaves on Nash manifolds. Compositio Math. 103 (1996) 31-62 (MR 97g:14039; Zbl 885.14029). With M. Coste and M. Shiota.

[1995b] Approximation in compact Nash manifolds. American J. Math. 117, no.4 (1995) 905-927 (MR 96f:32015; Zbl 873.32007). With M. Coste and M. Shiota.

[1995a] Algebraic versus analytic basicness. In Real Analytic and Algebraic Geometry, Proceedings Trento 1992, W. de Gruyter (1995) 1-19 (MR 96b:14068; Zbl 844.14024). With C. Andradas.

[1994e] Ubiquity of Lojasiewicz’s example of a non-basic semialgebraic set. Michigan Math. J. 41 (1994) 465-472 (MR 96e:14064; Zbl 844:14023). With C. Andradas.

[1994d] Problemas de algebricidad en topología diferencial. Homenaje al Prof. Etayo, Editorial Complutense (1994) 127-143 (MR 97c:57035; Zbl 820.57003).

[1994c] Low dimensional sections of basic semialgebraic sets. Illinois J. Math. 38, no.2 (1994) 303-326 (MR 95d:14056; Zbl 817:14034). With C. Andradas.

[1994b] On global Nash functions. Ann. Sc. Ec. Norm. Sup. Paris 27 (1994) 103-124 (MR 94m:14073; Zbl 805.14027). With M. Shiota.

[1994a] On local uniformization of orderings. In Recent advances in real algebraic geometry and quadratic forms, Proceedings of the RAGSQUAD year, Berkeley 1990-91, AMS Contemp. Math. 155 (1994) 19-46 (MR 94k:14048; Zbl 860.14043). With C. Andradas.

[1992] More on basic semialgebraic sets. In Real algebraic geometry, Proceedings Rennes-La Turballe 1991, Springer-Verlag LNM 1524 (1992) 128-139 (MR 94g:14030; Zbl 787.14036). With C. Andradas.

[1991b] On rings of semialgebraic functions. Math. Z. 206 (1991) 527-532 (MR 92f:14058; Zbl 745.14022). With J.M. Gamboa.

[1991a] Semialgebraic and semianalytic sets. Cahiers d’Histoire des Mathématiques, sér. 2, 1 (1991) 59-70 (MR 92m:14072; Zbl 746.14023).

[1990c] A characterization of sums of 2n-th powers of global meromorphic functions. Proc. AMS 109, no. 4 (1990) 915-923 (MR 90k:32035; Zbl 705.32003).

[1990b] On the topology of global semianalytic sets. In Real analytic and algebraic geometry, Proceedings Trento 1988, Springer-Verlag LNM 1420 (1990) 237-246 (MR 91d:32016; Zbl 723.14041).

[1990a] Some remarks on pythagorean real curve germs. J. Algebra 128, no.1 (1990) 271-275 (MR 91b:14072; Zbl 718.14027). With A. Campillo.

[1989b] A going-down theorem for real spectra. J. Algebra 124, no.2 (1989) 278-283 (MR 91g:14056; Zbl 688.14020).

[1989a] A dimension theorem for real spectra. J. Algebra 124, no.2 (1989) 271-277 (MR 91a:14036; Zbl 688.14021).

[1988b] On the connected components of a global semianalytic set. J. reine angew. Math. 392 (1988) 137-144 (MR 90h:32016; Zbl 645.32004).

[1988a] Minimal generation of basic open semianalytic sets. Invent. math. 92 (1988) 409-430 (MR 89f:32016; Zbl 655.32011). With C. Andradas and L. Bröcker.

[1987] Generalized Thom’s lemma in semianalytic geometry. Bull. Ac. Polonaise Sc. 35 (1987) 297-301 (MR 89b:32015; Zbl 634.32008). With F. Fernández and T. Recio.

[1986e] On the real spectrum of a ring of global analytic functions. Publ. IRMAR 4 (1986) 84-95 (MR 91e:14050; Zbl 634.14015).

[1986d] Basic properties of real analytic and semianalytic germs. Publ. IRMAR 4 (1986) 29-51 (MR 89h:32016; Zbl 634.32007).

[1986c] Cônes locaux et complétions. C. R. Ac. Sc. Paris 302, no.2 (1986) 67-69 (MR 87i:14005; Zbl 591.13017).

[1986b] On the homology of metacyclic coverings. Math. Ann. 275 (1986) 163-168 (MR 87i:57002; Zbl 578.57001). With A. Costa.

[1986a] A remark on fields with the dense orbits property. Pacific J. Math. 121 (1986) 189-192. (MR 87c:32011; Zbl 547.12015).

[1985c] On Hilbert’s 17th problem and real Nullstellensatz for global analytic functions. Math. Z. 190 (1985) 447-454 (MR 87b:32010; Zbl 579.14021).

[1985b] Pythagorean real curve germs. J. Algebra 94 (1985) 126-144 (MR 87c:13032; Zbl 611.14023).

[1985a] On orderings in real surfaces. J. Pure Appl. Algebra 36 (1985) 1-14 (MR 86g:12005; Zbl 559.14015). With M.E. Alonso and J.M. Gamboa.

[1984d] A note on a separation problem. Arch. Math. 43 (1984) 422-426 (MR 86f:32007; Zbl 547.14017).

[1984c] On pythagorean real irreducible algebroid curves. Rocky Mountain J. Math. 14 (1984) 899-901 (MR 86h:14018; Zbl 575.14020).

[1984b] Central orderings in fields of real meromorphic function germs. Manuscripta math. 46 (1984) 193-214 (MR 85c:58011; Zbl 538.14018).

[1984a] Ôrdres sur les surfaces réelles. C. R. Ac. Sc. Paris 298 (1984) 17-19 (MR 85b:32009; Zbl 587.14011). With M.E. Alonso and J.M. Gamboa.

[1982] On sequentially compact T2 compactifications. Topology and appl. 13 (1982) 177-189 (MR 83a:54027; Zbl 483.54016).

[1980] Sobre álgebras de Nash. Publ. Univ. Autónoma de Barcelona 20 (1980) 199-203 (MR 86h:32009).