Positive Polynomials by Alexander Prestel
Positivity 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 DEGRESn 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 a-
The Higher Infinite
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Fredholm Theory in Topological Vector Spaces
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Combinatorial Set Theory of C*-Algebras
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Classical Lie Algebras at Infinity
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Representation Theory of Finite Group Extensions
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Geometric Approximation Theory
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Determinants, Grobner Bases and Cohomology
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Topics in Global Real Analytic Geometry
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Mathematical Methods for Elastic Plates
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Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
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The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations
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The Riordan Group and Applications
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Domination in Graphs: Core Concepts
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Real Algebraic Varieties
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Curvature Measures of Singular Sets
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Structure and Regularity of Group Actions on One-Manifolds
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Superconcentration and Related Topics
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Extremal Polynomials and Riemann Surfaces
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Simplicial Partitions with Applications to the Finite Element Method
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Modular Forms
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Microstructured Materials: Inverse Problems
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Projective and Cayley-Klein Geometries
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Monotone Complete C*-algebras and Generic Dynamics
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Logical Foundations of Mathematics and Computational Complexity
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Arithmetic of Quadratic Forms
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Hardy Spaces on the Euclidean Space
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Functional Analytic Techniques for Diffusion Processes
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Harnack's Inequality for Degenerate and Singular Parabolic Equations
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Structure and Geometry of Lie Groups
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Inverse Linear Problems on Hilbert Space and their Krylov Solvability
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Modular Forms: Basics and Beyond
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The Absolute Galois Group of a Semi-Local Field
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Hardy Operators, Function Spaces and Embeddings
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Random Fields and Geometry
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Classical Fine Potential Theory
From the reviews of the first edition:
"This is a nicely written introduction to ‘reality’ and ‘positivity’ in rings, and besides students and researchers it can also be interesting for anyone who would like to learn more on positivity and orderings" (Vilmos Totik, Acta Scientiarum Mathematicarum, Vol. 68, 2002)
"A book on ‘real algebra’ that serves as an introduction to the subject in addition to the main theme of the text. … Well written with exercises for every chapter." (ASLIB Book Guide, Vol. 66 (11), 2001)
| SKU | Unavailable |
| ISBN 13 | 9783642074455 |
| ISBN 10 | 3642074456 |
| Title | Positive Polynomials |
| Author | Alexander Prestel |
| Series | Springer Monographs In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2011-09-22 |
| Number of pages | 268 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |