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Elementary Functional Analysis (Dover Books on Mathematics)
Feedback post: Moderator review and reinstatement processes. Why did my reputation suddenly increase by points? Related Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series. Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral.
Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis.
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Join our Signed First Edition Club or give a gift subscription for a signed book of great literary merit, delivered to you monthly. The final two chapters essentially comprise an introduction to Fourier analysis.
In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform. Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.
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