000			02271nmm a22002775i 4500
005			20230705150643.0
008			130409s2001 gw | s |||| 0|eng d
020			_a9783662046487 _9978-3-662-04648-7
082			_a512 _223
100			_aPrestel, Alexander. _920800
245			_aPositive Polynomials _h[electronic resource] : _bFrom Hilbert's 17th Problem to Real Algebra / _cby Alexander Prestel, Charles Delzell.
250			_a1st ed. 2001.
260			_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2001.
300			_aVIII, 268 p. _bonline resource.
505			_a1. Real Fields -- 2. Semialgebraic Sets -- 3. Quadratic Forms over Real Fields -- 4. Real Rings -- 5. Archimedean Rings -- 6. Positive Polynomials on Semialgebraic Sets -- 7. Sums of 2mth Powers -- 8. Bounds -- Appendix: Valued Fields -- A.1 Valuations -- A.2 Algebraic Extensions -- A.3 Henselian Fields -- A.4 Complete Fields -- A.5 Dependence and Composition of Valuations -- A.6 Transcendental Extensions -- A.7 Exercises -- A.8 Bibliographical Comments -- References -- Glossary of Notations.
520			_aPositivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilbert's 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra.
650			_aAlgebra. _920801
650			_aAlgebraic geometry. _920802
650			_aFunctional analysis. _920803
650			_aAlgebra. _920801
650			_aAlgebraic Geometry. _920804
650			_aFunctional Analysis. _920805
700			_aDelzell, Charles. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _920806
856			_uhttps://doi.org/10.1007/978-3-662-04648-7
942			_cEBK
999			_c13681 _d13681