Francesca Acquistapace, Fabrizio Broglia, José F. Fernando

Topics in Global Real Analytic Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book provides an exposition of the theory of analytic C-spaces developed by Cartan, Whitney and Tognoli and describes some central results in global real analytic geometry, such as Nullstellensatze and Positivstellensatze, including Forster's global Nullstellensatz for Stein algebras. It emphasizes the central role of Hilbert's 17th Problem in this context, devoting a chapter to the state of the art on this difficult problem. The focus then turns to a class of semianalytic sets defined by countably many global real analytic functions, which is stable under topological operations and satisfies a direct image theorem. A smaller subclass admits a decomposition into irreducible components comparable to that for semialgebraic sets. The last chapter is dedicated to the extension of some of the preceding results to smooth functions and quasi-analytic Denjoy-Carleman functions. The book is addressed to researchers and Ph.D students interested in complex analysis and real analytic geometry.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 273
• Erscheinungstermin: 7. Juni 2022
• Englisch
• ISBN-13: 9783030966669
• Artikelnr.: 64157155

Autorenporträt

Francesca Acquistapace was associate professor at the Mathematics Department of Pisa University from 1982 until her retirement in 2017. Previously, from 1974, she was assistant professor at the same department, where she presently has a research contract. She has given Ph.D courses in several universities, including in Madrid, Nagoya, Sapporo and the Poincaré Institute, Paris. Her research is in real analytic geometry, mainly in collaboration with the Spanish team (Andradas, Ruiz, Fernando) and with M. Shiota at Nagoya University.

Fabrizio Broglia was full professor at the Mathematics Department of Pisa University from 2001 until his retirement in 2018. Previously he was assistant and associate professor at the same Department, where he presently has a research contract. He was director of the Ph.D school of Science from 2002 until 2016. He was responsible in Italy for two European networks in Real Algebraic and Analytic Geometry (RAAG). His research deals with real analytic geometry, in collaboration with many colleagues, in particular the Spanish team.

José F. Fernando has been Professor at the Universidad Complutense de Madrid since February 2021. He has actively worked in Real Algebraic and Analytic Geometry (RAAG) with groups in Spain (Baro, Gamboa, Ruiz, Ueno), Duisburg-Konstanz (Scheiderer), Pisa (Acquistapace-Broglia), Rennes (Fichou-Quarez), and Trento (Ghiloni). He has established a strong collaboration and friendship with the Pisa RAAG group since 2003.

Inhaltsangabe

Introduction

Chapter 1. The class of C-analytic spaces

Chapter 2. More on analytic sets

Chapter 3. Nullstellensätze

Chapter 4. The 17th Hilbert's Problem for real analytic functions

Chapter 5. Analytic inequalities

References

Rezensionen

"The book presents nice results in the overlapping of real analytic geometry, complex analytic geometry and real algebraic geometry. It is well written. The introduction describes the historical developments in a very motivating way. The existing literature is well addressed. The book is intended for researchers or PhD students with a background in complex analysis (in several variables) and commutative algebra. It is dedicated to the memory of Alberto Tognoli." (Tobias Kaiser, Mathematical Reviews, June, 2023)

"This noteworthy book fulfills the goal of giving an excellently well written account of the present state of a number of relevant topics in the field of Real Analytic Geometry." (José Javier Etayo, zbMATH 1495.14001, 2022)