harmonic summability
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scholarly journals Pythagorean harmonic summability of Fourier series

2021 ◽  
Vol 54 (1) ◽  
pp. 212-232
Author(s):  
Nassar H. S. Haidar
Keyword(s):  
Fourier Series ◽  
Kalman Filtering ◽  
Harmonic Mean ◽  
Asymptotic Approach ◽  
Smoothing Operator ◽  
New Concepts ◽  
Summability Of Fourier Series ◽  
Harmonic Summability

Abstract 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. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach.

scholarly journals LACUNARY STATISTICAL HARMONIC SUMMABILITY

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Fatih Nuray ◽  
Keyword(s):  
Harmonic Summability

On a Tauberian theorem for absolute harmonic summability

1969 ◽  
Vol 65 (1) ◽  
pp. 93-99 ◽  
Author(s):  
O. P. Varshney ◽  
Govind Prasad
Keyword(s):  
Infinite Series ◽  
Tauberian Theorem ◽  
Partial Sums ◽  
Image Position ◽  
Harmonic Summability

Let Σan be a given infinite series with the sequence of partial sums {Sn}. Let the sequence be defined bywhere is given by

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