Topics in Global Real Analytic Geometry

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.

• IntroductionChapter 1. The class of C-analytic spaces Chapter 2. More on analytic setsChapter 3. NullstellensätzeChapter 4. The 17th Hilbert’s Problem for real analytic functionsChapter 5. Analytic inequalitiesReferences

“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)