A Gentle Invitation to the Fractional World
暫譯: 溫柔邀請進入分數世界
Abatangelo, Nicola, Dipierro, Serena, Valdinoci, Enrico
- 出版商: Springer
- 出版日期: 2025-10-28
- 售價: $2,550
- 貴賓價: 9.5 折 $2,423
- 語言: 英文
- 頁數: 257
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3032029511
- ISBN-13: 9783032029515
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相關分類:
微積分 Calculus
海外代購書籍(需單獨結帳)
相關主題
商品描述
The book focuses on the basic theory of nonlocal and fractional operators and it is divided into two main parts covering respectively the basic theory of the "singular-integral" fractional Laplacian operator, which also includes a number of explicit examples of its evaluations, and the regularity theory in L^p spaces, by going through Bessel and Besov spaces. A number of appendices then go over additional material in order to make the exposition as self-contained as possible.
The book is suitable for a PhD course but can be also read by advanced undergraduates. It contains didactic elements, but it is also useful for researchers, since it collects essential material in a concise and self-constrained way.
商品描述(中文翻譯)
本書專注於非局部和分數算子的基本理論，分為兩個主要部分，分別涵蓋「奇異積分」分數拉普拉斯算子的基本理論，並包括其評估的多個明確範例，以及在 L^p 空間中的正則性理論，通過 Bessel 和 Besov 空間進行探討。書中還附有多個附錄，以便使內容盡可能自足。
本書適合用作博士課程，但也適合高年級本科生閱讀。它包含教學元素，但對於研究人員來說也很有用，因為它以簡潔且自我約束的方式收集了重要的材料。
作者簡介
Nicola Abatangelo is an associate professor of Mathematical Analysis at the University of Bologna (Italy) since September 2024. Previously he has been assistant professor in the same university, a Humboldt post-doctoral fellow at the University of Frankfurt (Germany), and a post-doc at the Universities of Zurich (Switzerland) and Brussels (Belgium). He has obtained his PhD from the Universities of Amiens (France) and Milan (Italy) in 2015. His research focuses on the analysis of fractional Laplacian type operators, with particular emphasis on nonlocal elliptic PDEs and the qualitative properties of the associated solutions.
Serena Dipierro is a Professor of Mathematics, Fellow of the Australian Mathematical Society, and Australian Mathematical Society Hanna Neumann Lecturer. She carried out her academic career in Santiago de Chile, Edinburgh, Magdeburg, Berlin, Melbourne, Milan, and Perth. She has obtained prestigious awards, including the Australian Mathematical Society Medal, the Mahony-Neumann-Room Prize, the Bartolozzi Prize of the Italian Mathematical Union, the Christopher Heyde Medal of the Australian Academy of Science, the Book Prize of the Italian Mathematical Union, and the Prize of the Bulletin of the Brazilian Mathematical Society.
Enrico Valdinoci is a Professor of Mathematics and Australian Laureate Fellow. He carried out his academic career in Pisa, Rome, Milan, Berlin, Melbourne, and Perth. He is a highly cited researcher, Ladyzhenskaya Lecturer and has been awarded the James S. W. Wong Prize, the Mahony-Neumann-Room Prize, the Orazio Arena Prize, the Book Prize of the Unione Matematica Italiana, the Prize of the Bulletin of the Brazilian Mathematical Society, and the Amerio Gold Medal Prize.
作者簡介(中文翻譯)
尼科拉·阿巴坦傑洛自2024年9月起擔任意大利博洛尼亞大學數學分析副教授。此前，他曾在同一所大學擔任助理教授，並在德國法蘭克福大學擔任洪堡博士後研究員，以及在瑞士蘇黎世大學和比利時布魯塞爾大學擔任博士後研究員。他於2015年在法國亞眠大學和意大利米蘭大學獲得博士學位。他的研究專注於分數拉普拉斯型算子的分析，特別強調非局部橢圓偏微分方程及其相關解的質量特性。
塞雷娜·迪皮耶羅是數學教授，澳大利亞數學學會會員，並擔任澳大利亞數學學會哈娜·紐曼講師。她的學術生涯遍及智利聖地亞哥、愛丁堡、馬格德堡、柏林、墨爾本、米蘭和珀斯。她獲得了多項著名獎項，包括澳大利亞數學學會獎章、馬霍尼-紐曼-魯姆獎、意大利數學聯盟的巴托洛齊獎、澳大利亞科學院的克里斯托弗·海德獎、意大利數學聯盟的書籍獎，以及巴西數學學會公告的獎項。
恩里科·瓦爾迪諾奇是數學教授及澳大利亞榮譽研究員。他的學術生涯遍及比薩、羅馬、米蘭、柏林、墨爾本和珀斯。他是一位高被引研究者，曾擔任拉迪任斯卡亞講師，並獲得詹姆斯·S·W·黃獎、馬霍尼-紐曼-魯姆獎、奧拉齊奧·阿雷納獎、意大利數學聯盟的書籍獎、巴西數學學會公告的獎項，以及阿梅里奧金獎。
