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Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view. TOC:Contents: General Topology.- Banach Spaces.- Hilbert Spaces.- Spectral Theory.- Unbounded Operators.- Integration Theory.- Bibliography.- List of Symbols.- Index.

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This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

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Vol. 1 of Lars Hörmander´s influential 4-volume treatise is a detailed exposition of the theory of distributions. From the reviews: ´´In order to illustrate the richness of the book: in my review of the 1983 edition [...] I gave a list of 20 subjects which were new compared to Hörmander´s book of 1963. Most of these subjects concern important, basic and highly nontrivial theorems in analysis. Hörmander´s treatment of these is extremely clear and efficient and often highly original. [...] Most of the exercises are witty, with an interesting point. The phrasing of both the exercises and the answers and hints is very careful [...] In all, the book can be highly recommended, both as a textbook for advanced students, and as background and reference for introductory courses on distributions and Fourier analysis.´´ - J.J. Duistermaat in Mededelingen van het Wiskundig Genootschap. The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

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A detailed analysis of Porsche AG and its industry segment: Angela Amor

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A Detailed Analysis of the Constitution:Seventh Edition Edward F. Cooke

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A detailed analysis of Porsche AG and its industry segment:Akademische Schriftenreihe. 1. Auflage. Angela Amor

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KNN Classifier and K-Means Clustering for Robust Classification of Epilepsy from EEG Signals. A Detailed Analysis: Harikumar Rajaguru, Sunil Kumar Prabhakar

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A Detailed Analysis of Research in the U. S. Department of Agriculture, as Related to the Report, an Evaluation of Agricultural Research:For Use of Department Scientists and Their Cooperators (Classic Reprint) U. S. Agricultural Research Service

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Detailed Genetic Analysis of a Wide Faba Bean (Vicia faba L.) Cross ”German x Moroccan“:

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