Function Convergence

Vicente Montesinos (), Peter Zizler () and Václav Zizler ()
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Vicente Montesinos: Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada
Peter Zizler: Mount Royal University, Department of Mathematics, Physics and Engineering
Václav Zizler: University of Alberta, Department of Mathematical and Statistical Sciences

Chapter 5 in An Introduction to Modern Analysis, 2015, pp 215-281 from Springer

Abstract: Abstract The study of sequences of functions is central in Analysis. On one hand, many functions we are working with can be defined as limits of sequences of elementary functions (polynomials, trigonometric polynomials, etc.). On the other hand, it may be convenient to approximate a given function by functions that have good properties in order to simplify computations or whole theories. The purpose of this chapter is to investigate all this. We shall consider a sequence $\{f_n\}_{n=1}^{\infty}$ of real-valued functions defined on a certain nonempty subset D of ${\mathbb R}$ . We shall say that D is a common domain for all the functions f n of the sequence.

Keywords: Textbf; Baire Class; Taylor Polynomial; Cauchy Criterion; Cauchy-Hadamard Formula (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-12481-0_5

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