Topics in Global Real Analytic Geometry
Acquistapace, Francesca, Broglia, Fabrizio, Fernando, José F.
- 出版商: Springer
- 出版日期: 2023-06-09
- 售價: $5,160
- 貴賓價: 9.5 折 $4,902
- 語言: 英文
- 頁數: 273
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030966682
- ISBN-13: 9783030966683
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商品描述
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert's problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert's problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer.
In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. During the redaction some proofs have been simplified with respect to the original ones.
商品描述(中文翻譯)
在前兩章中，我們回顧了Cartan、Whitney和Tognoli所發展的理論。然後，我們證明了Stein代數和C-解析空間上的實解析函數代數的Nullstellensatz。在這裡，我們找到了實數Nullstellensatz和第17個希爾伯特問題（關於正半定解析函數）之間的關係。換句話說，對希爾伯特問題的肯定回答意味著對實數Nullstellensatz的解更接近於實多項式的解。一章專門討論了這個問題的最新研究狀況，但仍然遠未完全解答。
在最後一章中，我們討論了不等式。我們描述了一類由可數多個全局實解析函數定義的半解析集，這類集合在拓撲性質和斯坦空間之間的適當全純映射下是穩定的，即滿足直接映射定理。一個更小的類別也可以像半代數集合一樣分解成不可約分的組件。在編寫過程中，一些證明已經相對於原始證明簡化了。
作者簡介
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.
作者簡介(中文翻譯)
Francesca Acquistapace自1982年起擔任比薩大學數學系副教授，直到2017年退休。在此之前，她於1974年起在同一系所擔任助理教授，目前仍有研究合約。她曾在多所大學授課，包括馬德里、名古屋、札幌和波安卡雷研究所巴黎分所。她的研究主要集中在實解析幾何，主要與西班牙團隊（Andradas、Ruiz、Fernando）以及名古屋大學的M. Shiota合作。
Fabrizio Broglia自2001年起擔任比薩大學數學系教授，直到2018年退休。在此之前，他曾在同一系所擔任助理教授和副教授，目前仍有研究合約。他曾於2002年至2016年擔任科學博士學院的主任。他在意大利負責兩個歐洲實代數和解析幾何（RAAG）網絡。他的研究涉及實解析幾何，與許多同事合作，尤其是與西班牙團隊合作。
José F. Fernando自2021年2月起擔任馬德里康普頓斯大學教授。他在實代數和解析幾何（RAAG）方面與西班牙（Baro、Gamboa、Ruiz、Ueno）、杜伊斯堡-康斯坦茨（Scheiderer）、比薩（Acquistapace-Broglia）、雷恩（Fichou-Quarez）和特倫托（Ghiloni）的團隊積極合作。自2003年以來，他與比薩RAAG團隊建立了密切的合作和友誼。
