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Titlebook: A Course in Functional Analysis and Measure Theory; Vladimir Kadets Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010): 46-01, 4

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發(fā)表于 2025-3-21 18:25:50 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱(chēng)A Course in Functional Analysis and Measure Theory
影響因子2023Vladimir Kadets
視頻videohttp://file.papertrans.cn/141/140472/140472.mp4
發(fā)行地址Provides necessary preliminaries.Explores basic and advanced material in functional analysis and operator theory, including applications to Fourier series and the Fourier transform.Includes over 1500
學(xué)科分類(lèi)Universitext
圖書(shū)封面Titlebook: A Course in Functional Analysis and Measure Theory;  Vladimir Kadets Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010): 46-01, 4
影響因子.Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis...Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory..Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses..
Pindex Textbook 2018
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Reihe Interkulturelle Philosophiee intrinsic metric of a surface are studied), and also, it goes without saying, in topology courses. For this reason, we only briefly recall the well-known definitions and facts, discuss the terminology and notation adopted in this book, while dwelling in more detail on issues that possibly are not treated in other courses.
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https://doi.org/10.1007/978-3-476-05832-4algebras of sets; Borel sets; finite and countable additivity of measures; atoms, atomic and non-atomic measures; extension of measures; the Lebesgue measure on the interval and on the real line; Lebesgue’s theorem on the differentiability of monotone functions.
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Reihe Interkulturelle Philosophie analogy with the Riemann integral, in this book the theory of the Lebesgue integral is treated on the basis of Fréchet’s definition, namely, by means of the convergent integral sums analogous to the Riemann integral sums. One of the advantages of this approach is the simplicity with which this definition extends to vector-valued functions.
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Reihe Interkulturelle Philosophie traditionally regarded as one of the “fundamental principles of functional analysis”. Such “fundamental principles” also include the geometric form of the Hahn–Banach theorem (Chapter 9), Banach’s inverse operator theorem, the open mapping and the closed graph theorems, as well as the Banach–Steinhaus theorem (Chapter 10).
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