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A Summation Method for Trigonometric Fourier Series Based on Sinc-Approximations
We propose a summation method for trigonometric Fourier series. We use the sequential approach for defining generalized functions. The method makes...
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Fourier Series
In this chapter we consider the representations of functions in the form of series in trigonometric functions. This approach will be used for solving...
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Fourier Series
Chapter 1 covers the classical theory of Fourier series of...
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Trigonometric series and the permutation sign convergence condition
We prove that a uniformly convergent trigonometric series may not satisfy the permutation sign convergence condition, hence it may not satisfy the...
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Fourier Series
In Chap. 4 we discuss the expansion of periodic functions into infinite trigonometric series (introduced by Joseph Fourier in the early 1800s)....
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Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals
It is well known that Luzin’s conjecture has a positive solution for one-dimensional trigonometric Fourier series, but in the multidimensional case...
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Fourier Series and Gauss Sums
The basic functions that we will be concerned with in this chapter are for $$n...
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Almost everywhere divergence of Cesàro means of subsequences of partial sums of trigonometric Fourier series
In this paper, we investigate the relationship between pointwise convergence of the arithmetic means corresponding to the subsequence of partial...
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Fourier Series
The chapter is an introduction to the theory of Fourier series. We present here some aspects of Fourier series as applicable to practical problems in...
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On Fourier Series Almost Universal in the Class of Measurable Functions
AbstractIn this work, a universal trigonometric series is constructed such that, after multiplying the terms of this series by some sequence of signs
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Random Fourier Series and Trigonometric Sums
We solve the long-standing problem of finding necessary and sufficient conditions for the convergence of random trigonometric series with independent...
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On Almost Universal Double Fourier Series
The first examples of universal trigonometric series in the class of measurable functions were constructed by D. E. Men’shov. As follows from...
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Fourier Series
This chapter deals in more detail with the Fourier series in the three alternative forms as the sum of shifted cosine functions (“physical”...
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On the Summability of Fourier Series by the Generalized Cesáro Method
AbstractThe analog of the Lebesgue–Gergen convergence test for generalized Cesáro means of Fourier trigonometric series is given.
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On the Convergence Fourier Series and Greedy Algorithm by Multiplicative System
In this work we discuss the behavior of Fourier coefficients with respect to the multiplicative system (Vilenkin system), as well as convergence of...