A primer on Hilbert space theory linear spaces, topological spaces, metric spaces, normed spaces, and topological groups / [electronic resource] :

• 作者： Alabiso, Carlo.
• 其他作者：
  • Weiss, Ittay.
  • SpringerLink (Online service)
• 其他題名：
  • UNITEXT for physics.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 版本：Second edition.
• 叢書名： UNITEXT for physics,
• 主題： Hilbert space. , Topological spaces. , Metric spaces. , Normed linear spaces. , Mathematical Methods in Physics. , Functional Analysis. , Algebraic Topology.
• ISBN： 9783030674175 (electronic bk.) 、 9783030674168 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 1. Hilbert Space Theory - A Quick Overview -- 2. Linear Spaces -- 3. Topological Spaces -- 4. Metric Spaces -- 5. The Lebesgue Integral Following Mikusiniski -- 6. Banach Spaces -- 7. Hilbert Spaces -- 8. A Survery of mathematical structures related to Hilbert space theory -- 9. Solved Problems.
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• 摘要註: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors's lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
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