Smale 17th Problem: Advances and Open Directions

New Zealand Journal of Mathematics ◽

10.53733/92 ◽

2021 ◽

Vol 52 ◽

pp. 233-257

Author(s):

Felipe Cucker

Keyword(s):

17Th Problem

We give an overview of Smale's 17th problem describing the context in whichSmale proposed it, the ideas that led to its solution, and the extensionsand subsequent progress after this solution.

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A continuous and rational solution to Hubert’s 17th problem and several cases of the Positivstellensatz

Computational Algebraic Geometry ◽

10.1007/978-1-4612-2752-6_5 ◽

1993 ◽

pp. 61-75 ◽

Cited By ~ 3

Author(s):

Charles N. Delzell ◽

Laureano González-Vega ◽

Henri Lombardi

Keyword(s):

Rational Solution ◽

17Th Problem

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Hilbert’s 17th Problem. Quadratic Forms in Real Algebraic Geometry

Real Algebraic Geometry ◽

10.1007/978-3-662-03718-8_7 ◽

1998 ◽

pp. 103-131

Author(s):

Jacek Bochnak ◽

Michel Coste ◽

Marie-Françoise Roy

Keyword(s):

Algebraic Geometry ◽

Quadratic Forms ◽

Real Algebraic Geometry ◽

17Th Problem

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Smale’s 17th Problem: I

Grundlehren der mathematischen Wissenschaften - Condition ◽

10.1007/978-3-642-38896-5_17 ◽

2013 ◽

pp. 331-365

Author(s):

Peter Bürgisser ◽

Felipe Cucker

Keyword(s):

17Th Problem

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Some concrete aspects of Hilbert’s 17th Problem

Real Algebraic Geometry and Ordered Structures - Contemporary Mathematics ◽

10.1090/conm/253/03936 ◽

2000 ◽

pp. 251-272 ◽

Cited By ~ 164

Author(s):

Bruce Reznick

Keyword(s):

17Th Problem

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Hilbert's 17th Problem

Quadratic Forms with Applications to Algebraic Geometry and Topology ◽

10.1017/cbo9780511526077.007 ◽

1995 ◽

pp. 75-93

Keyword(s):

17Th Problem

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An elementary and constructive solution to Hilbert's 17th Problem for matrices

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-07-09068-5 ◽

2008 ◽

Vol 136 (01) ◽

pp. 73-77 ◽

Cited By ~ 12

Author(s):

Christopher J. Hillar ◽

Jiawang Nie

Keyword(s):

Constructive Solution ◽

17Th Problem

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The Procesi–Schacher conjecture and Hilbert's 17th problem for algebras with involution

Journal of Algebra ◽

10.1016/j.jalgebra.2010.03.022 ◽

2010 ◽

Vol 324 (2) ◽

pp. 256-268 ◽

Cited By ~ 5

Author(s):

Igor Klep ◽

Thomas Unger

Keyword(s):

17Th Problem

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Kalman—Yakubovich—Popov Lemma And Hilbert's 17th Problem∗∗Supported by SPbSU, grant 6.38.230.2015.

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2015.09.190 ◽

2015 ◽

Vol 48 (11) ◽

pp. 238-241

Author(s):

Sergei V. Gusev

Keyword(s):

17Th Problem

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Continous, piecewise-polynomial functions which solve Hilbert's 17th problem.

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.1993.440.157 ◽

1993 ◽

Vol 1993 (440) ◽

pp. 157-174 ◽

Cited By ~ 2

Keyword(s):

Polynomial Functions ◽

Piecewise Polynomial ◽

Piecewise Polynomial Functions ◽

17Th Problem

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On Hilbert’s 17th problem in low degree

Algebra & Number Theory ◽

10.2140/ant.2017.11.929 ◽

2017 ◽

Vol 11 (4) ◽

pp. 929-959 ◽

Cited By ~ 2

Author(s):

Olivier Benoist

Keyword(s):

Low Degree ◽

17Th Problem

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