Titlebook: An Introduction to Basic Fourier Series; Sergei K. Suslov Book 2003 Springer Science+Business Media Dordrecht 2003 Complex analysis.Hyperg

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含糊

Introduction of Basic Fourier Series,Our main objective in this chapter is to define basic Fourier series and to establish some elementary facts about them. In our presentation most of the material can be read independently from Chapters 3 and 4, we only assume that the reader is familiar with the basic exponential and basic trigonometric functions covered in Chapter 2.

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Improved Asymptotics of Zeros,In Section 6.3 we derived the asymptotic formulas (6.3.14) and (6.3.15) for the zeros of the basic sine .. (.) and basic cosine .. ((.)) functions, respectively. In this chapter we shall find improved asymptotics for these zeros by a different method using the Lagrange inversion formula.

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Basic Exponential and Trigonometric Functions,monic motion on a .-quadratic grid. Some of their elementary properties will be derived in order to form the basis for developing the theory of basic Fourier series and study some of their applications in the subsequent chapters.

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Investigation of Basic Fourier Series,gonometric systems, and will establish several convenient tools, such as asymptotics of zeros, which are important for practical investigation of these series in the next chapters. Methods of summation and a few explicit examples of .-Fourier series will be also discussed among other things.

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Sergei K. SuslovIncludes supplementary material:

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