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Pythagorean harmonic summability of Fourier series

open access: yesDemonstratio Mathematica, 2021
This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation ...
Haidar Nassar H. S.
doaj   +1 more source

MULTIPLE FOURIER SERIES AND FOURIER INTEGRALS WITH NON-SEPARABLE VARIABLES

open access: yesИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. Integral transforms for functions of several variables are an actively developing area of mathematical analysis. Numerous applications in integral transforms method for solving equations of mathematical physics, in signal processing of ...
O. E. Yaremko   +2 more
doaj   +1 more source

Generalization of the Hardy-Littlewood theorem on Fourier series

open access: yesҚарағанды университетінің хабаршысы. Математика сериясы, 2021
In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance.
S. Bitimkhan
doaj   +1 more source

Rapidly Converging Series for ζ(2n+1) from Fourier Series

open access: yesAbstract and Applied Analysis, 2014
Ever since Euler first evaluated ζ(2) and ζ(2m), numerous interesting solutions of the problem of evaluating the ζ(2m)  (m∈ℕ) have appeared in the mathematical literature.
Junesang Choi
doaj   +1 more source

On Fourier series

open access: yesJournal of Numerical Analysis and Approximation Theory, 1976
Not available.
G.P. Névai
doaj   +2 more sources

Fast Algorithms for the computation of Fourier Extensions of arbitrary length [PDF]

open access: yes, 2015
Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of overcoming these problems is by using a Fourier series on a larger domain, say $[-T,T]$ with $T>1$, a
Daan Huybrechs   +3 more
core   +3 more sources

Local properties of Fourier series

open access: yesInternational Journal of Mathematics and Mathematical Sciences, 2000
A theorem on local property of |N¯,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N¯,pn|k summability factors of Fourier series have been proved.
Hüseyin Bor
doaj   +1 more source

On (J,pn) summability of Fourier series

open access: yesInternational Journal of Mathematics and Mathematical Sciences, 1989
In this note two theorems have been established. The first one deals with the summability (J,pn) of a Fourier series while the second on concerns with the summability of the first derived Fourier series.
S. M. Mazhar
doaj   +2 more sources

Product Summability Transform of Conjugate Series of Fourier Series

open access: yesInternational Journal of Mathematics and Mathematical Sciences, 2012
A known theorem, Nigam (2010) dealing with the degree of approximation of conjugate of a signal belonging to Lipξ(t)-class by (E,1)(C,1) product summability means of conjugate series of Fourier series has been generalized for the weighted W(Lr,ξ(t)), (r ...
Vishnu Narayan Mishra   +2 more
doaj   +1 more source

On uniform convergence of Fourier series

open access: yes, 2012
We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e ...
A. Beurling   +5 more
core   +1 more source

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