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<div data-olk-copy-source="MailCompose"><p class="MsoNormal"><span style="mso-bidi-font-family: 'Times New Roman'; color: black;">This book provides an introduction to frame theory in Banach and Hilbert spaces, with a particular focus on the Banach space aspects of the frame theory and its applications. The authors present main developments from recent decades in the theory of frames, dilations, operator-valued measures, sampling, and related applications. By bridging topics from Banach space geometry, applied harmonic analysis, and quantum information theory, the book highlights a novel perspective: frame theory not only serves as a powerful and central tool in mathematics and engineering, but is also deeply intertwined with the structure and theory of Banach spaces. Rather than providing an exhaustive treatment, the book offers a broadly relevant and accessible overview that enables researchers across various fields to quickly grasp the foundational ideas and explore related research directions.</span></p></div>

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Banach Space Aspects of Frame Theory with Applications

  • 书籍

  • 发表日期：

    2026年

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  • Deguang Han,
  • Qianfeng Hu,
  • Bei Liu,
  • Rui Liu

摘要

This book provides an introduction to frame theory in Banach and Hilbert spaces, with a particular focus on the Banach space aspects of the frame theory and its applications. The authors present main developments from recent decades in the theory of frames, dilations, operator-valued measures, sampling, and related applications. By bridging topics from Banach space geometry, applied harmonic analysis, and quantum information theory, the book highlights a novel perspective: frame theory not only serves as a powerful and central tool in mathematics and engineering, but is also deeply intertwined with the structure and theory of Banach spaces. Rather than providing an exhaustive treatment, the book offers a broadly relevant and accessible overview that enables researchers across various fields to quickly grasp the foundational ideas and explore related research directions.