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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 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses. Springer Professional. Back to the search result list. Table of Contents Frontmatter Chapter 1. Metric and Topological Spaces Abstract.

Topological, and especially metric spaces, are frequently mentioned and used in courses on mathematical analysis, linear algebra in which one of the most important examples of metric spaces, the finite-dimensional Euclidean space, is examined , differential geometry in which geodesic curves and the 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.

The reader has undoubtedly already encountered the notion of measure, though perhaps under a different name. For instance, the area of a plane figure, the length of a rectifiable curve, the volume, the mass, are all examples of measures. Measurable functions play in measure theory the same role that continuous functions do in the theory of topological spaces.

MAT / MAT University of Toronto

The Lebesgue integral extends the Riemann integral to wider classes of functions. The definition of Lebesgue integral is a little bit more complicated, but the properties are much more convenient in applications. That is why the modern mathematics mainly uses the Lebesgue integral.

  1. Locally Convex Spaces over Non-Archimedean Valued Fields.
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One of the advantages of this approach is the simplicity with which this definition extends to vector-valued functions. About this product Product Information Focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus is not injective.

Harmonic Analysis of Operators on Hilbert Space

Additional Product Features Author s. Bela Szokefalvi-Nagy was a famed mathematician for his work in functional analysis and operator theory. He was the recipient of the Lomonosov Medal in He is well known for his work in operator theory, infinite dimensional dynamical systems, ergodic theory, as well as applications in such diverse fields as control theory, mathematical biology and mathematical economics. Hari Bercovici is currently a professor of mathematics at Indiana University.

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He works in operator theory and function theory. He made important contributions to operator theory, many of them represented in this monograph. Show more Show less.

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401-3461-00L Functional Analysis I

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