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On the convergence factor of a Fourier series and a differentiated Fourier series
Mathematical Proceedings of the Cambridge Philosophical Society, 1969Definition A. The serieswith partial sumUn (or the sequence {Un}) is said to be summable by logarithmic means to the sum U ...
B. K. Ray, R. Mohanty
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1966
Publisher Summary This chapter focuses on “function space” as opposed to a three-dimensional “vector space.” This function space is infinite dimensional, in the sense that an infinite sequence of mutually orthogonal functions is needed to represent an arbitrary function.
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Publisher Summary This chapter focuses on “function space” as opposed to a three-dimensional “vector space.” This function space is infinite dimensional, in the sense that an infinite sequence of mutually orthogonal functions is needed to represent an arbitrary function.
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On the Fourier series and Fourier transforms
Journal of Mathematical Sciences, 2019This survey article is addresses to classical harmonic analysis. In particular, a number of classical theorems are presented with the simplest, in our opinion, proofs (see also [1] and references therein). Some results of the present article are new and are published for the first time.
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Improved cellulose X-ray diffraction analysis using Fourier series modeling
Cellulose, 2020Wenqing Yao +2 more
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Forecasting tourism demand using fractional grey prediction models with Fourier series
Annals of Operations Research, 2020Yi-Chung Hu
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, 1977 In the subsequent sections use will be made of the expansion of given functions in Fourier series and it will be more convenient to represent them in complex form; some remarks will now be made about this.
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Periodic Hyperfunctions and Fourier Series Fourier Series
1992We have now almost finished the general discussion of hyperfunctions. From now on we shall attempt to apply this general theory to various cases. In this chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations.
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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly