Topics in Global Real Analytic Geometry
暫譯: 全球實解析幾何主題

Acquistapace, Francesca, Broglia, Fabrizio, Fernando, José F.

Topics in Global Real Analytic Geometry
  • 出版商: Springer
  • 出版日期: 2023-06-09
  • 售價: $5,260
  • 貴賓價: 9.5 折 $4,997
  • 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，我們回顧了由卡坦（Cartan）、惠特尼（Whitney）和托尼奧利（Tognoli）所發展的理論。接著，我們證明了 Nullstellensatz 在 Stein 代數和 C-解析空間上的實解析函數代數中的情況。在這裡，我們發現了實 Nullstellensatz 與第十七個希爾伯特問題（Hilbert's problem）之間的關係，該問題涉及正半定解析函數。具體而言，對希爾伯特問題的正面回答意味著對實 Nullstellensatz 的解決方案更類似於實多項式的情況。專門有一章討論這個問題的最新進展，但距離完整的答案仍然遙遠。

在最後一章中，我們處理不等式。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合，這類集合在拓撲性質和 Stein 空間之間的適當全純映射下是穩定的，即滿足直接映像定理。一個更小的類別也允許分解為不可約組件，這與半代數集合的情況相似。在撰寫過程中，某些證明相較於原始證明已經簡化。

作者簡介

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.

作者簡介(中文翻譯)

Francesca Acquistapace 自1982年起擔任比薩大學數學系的副教授，直到2017年退休。早在1974年，她便在同一系所擔任助理教授，目前仍持有研究合約。她曾在多所大學教授博士課程，包括馬德里、名古屋、札幌及巴黎的龐卡萊研究所。她的研究專注於實解析幾何，主要與西班牙團隊（Andradas、Ruiz、Fernando）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的正教授，直到2018年退休。之前，他在同一系所擔任助理教授及副教授，目前仍持有研究合約。他於2002年至2016年間擔任科學博士學校的主任。他在意大利負責兩個關於實代數與解析幾何（RAAG）的歐洲網絡。他的研究涉及實解析幾何，並與許多同事合作，特別是西班牙團隊。
José F. Fernando 自2021年2月起擔任馬德里康普頓斯大學的教授。他積極參與實代數與解析幾何（RAAG）的研究，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）及特倫托（Ghiloni）等地的團隊合作。自2003年以來，他與比薩的 RAAG 團隊建立了強大的合作關係和友誼。

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