The best approximation of a function and linear methods for the summation of Fourier series

1968 ◽  
pp. 127-147
Author(s):  
M. F. Timan
Keyword(s):  
Fourier Series ◽  
Best Approximation ◽  
The Best Approximation ◽  
Approximation Of A Function

scholarly journals Approximation of a Function in Hölder Class Using Double Karamata (Kλ,μ) Method

2020 ◽  
Vol 13 (3) ◽  
pp. 567-578
Author(s):  
H. K. Nigam ◽  
Md. Hadish
Keyword(s):  
Fourier Series ◽  
Best Approximation ◽  
Double Fourier Series ◽  
Hölder Class ◽  
The Best Approximation ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Approximation Of A Function

In this paper, we establish a new theorem on the best approximation of a function of two variables belonging to H ̈older class by double Karamata (Kλ,μ) means of its double Fourier series.

Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces

2006 ◽  
Vol 13 (2) ◽  
pp. 315-332
Author(s):  
István Mező
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Lebesgue Space ◽  
Best Approximation ◽  
Acta Math ◽  
Function Spaces ◽  
Vilenkin Group ◽  
Strong Connection ◽  
The Best Approximation

Abstract We rephrase Fridli's result [Fridli, Acta Math. Hungar. 45: 393–396, 1985] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [Gát, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 17: 161–169, 2001] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.

scholarly journals On the boundedness of the partial sums operator for the Fourier series in the function classes families associated with harmonic intervals

2021 ◽  
Vol 103 (3) ◽  
pp. 131-139
Author(s):  
Gulsim A. Yessenbayeva ◽  
◽  
Gulmira A. Yessenbayeva ◽  
A.T. Kasimov ◽  
N.K. Syzdykova ◽  
...  
Keyword(s):  
Fourier Series ◽  
Approximation Theory ◽  
Trigonometric Polynomials ◽  
Partial Sums ◽  
Practical Applications ◽  
Noise Interference ◽  
The Best Approximation ◽  
Function Classes ◽  
Main Components ◽  
Approximation Of A Function

The article is devoted to the study of some data from the theory of functions approximation by trigonometric polynomials with a spectrum from special sets called harmonic intervals. Due to the limited perception range of devices, the perception range of the senses of the person himself, when studying a mathematical model it is often enough to find an approximation of the object so that the error (noise, interference, distortion) is outside the interval of perception. Harmonic intervals model problems of this kind to some extent. In the article the main components of the approximation theory of functions by trigonometric polynomials with a spectrum from harmonic intervals are presented, the theorem on estimating the best approximation of a function by trigonometric polynomials through the best approximations of a function by trigonometric polynomials with a spectrum from harmonic intervals is proved. Theorems on the boundedness of the partial sums operator for the Fourier series in the function classes families associated with harmonic intervals are considered; such a theorem for the Lorentz space is generalized and proved. The article is mainly aimed at scientific researchers dealing with practical applications of the approximation theory of functions by trigonometric polynomials with a spectrum from special sets.

scholarly journals Approximation of Functions in Besov Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Hare Krishna Nigam ◽  
Supriya Rani
Keyword(s):  
Fourier Series ◽  
Besov Space ◽  
Best Approximation ◽  
Approximation Of Functions ◽  
Approximation Of A Function

In the present paper, we establish a theorem on best approximation of a function g ∈ Bqλ(Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1.

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

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