The absolute convergence of the Fourier-Haar series for two-dimensional functions

2008 ◽  
Vol 52 (5) ◽  
pp. 9-19 ◽  
Author(s):  
L. D. Gogoladze ◽  
V. Sh. Tsagareishvili
Keyword(s):  
Absolute Convergence ◽  
Two Dimensional ◽  
Haar Series ◽  
The Absolute

On the absolute convergence of Fourier series with respect to general orthonormal systems

2017 ◽  
Vol 24 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Vakhtang Tsagareishvili
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
Haar Series ◽  
The Absolute

AbstractThe problems of absolute convergence of multiple Fourier series with respect to both general orthonormal systems and multiple Haar series are studied.

scholarly journals Continued Fractions with Absolutely Convergent Even or Odd Part

1959 ◽  
Vol 11 ◽  
pp. 131-140 ◽  
Author(s):  
David F. Dawson
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Absolute Convergence ◽  
The Absolute

The purpose of this paper is to give conditions under which the absolute convergence of the subsequence of odd or of even approximants to a continued fraction implies convergence of the continued fraction. In § 2 we consider the problem in general, and in § 3 we impose a condition which gives absolute convergence of the odd or of the even part of the continued fraction and state conditions which imply convergence of the continued fraction.

The Relationship between the Letters of Al-Iḫlāṣ (Q 112:1-4) and Their Iterations Using B-Spline Function

2019 ◽  
Vol 17 (1) ◽  
pp. 60-86
Author(s):  
Faoziya S.M. Musbah
Keyword(s):  
Spline Function ◽  
Piecewise Linear ◽  
Two Dimensional ◽  
B Spline ◽  
Holy Quran ◽  
Data Points ◽  
The Holy Quran ◽  
The Absolute ◽  
Unity Of God ◽  
The Relationship

Abstract Al-Iḫlāṣ is an important chapter within the Holy Quran (words of God) because it is a brief declaration of the absolute unity of God (Allah). This paper analyzes al-Iḫlāṣ mathematically in order to gain an understanding of the relationship between the letters of this chapter and their iterations. The analyzed two-dimensional data points (xi,yi) define a piecewise linear curve that is shaped like Allah’s name as it is written in Arabic. The B-spline function is used to analyze this data so as to obtain a second degree curve.

Sign in / Sign up

Export Citation Format

Share Document