On |C, 1| summability factors of power series and Fourier series

1962 ◽  
Vol 80 (1) ◽  
pp. 265-268 ◽  
Author(s):  
C. T. Rajagopal
Keyword(s):  
Fourier Series ◽  
Power Series ◽  
Summability Factors

The summability factors of a Fourier series

1957 ◽  
Vol 24 (1) ◽  
pp. 103-117 ◽  
Author(s):  
B. N. Prasad ◽  
S. N. Bhatt
Keyword(s):  
Fourier Series ◽  
Summability Factors

Uniform summability of power series

1972 ◽  
Vol 71 (2) ◽  
pp. 335-341 ◽  
Author(s):  
J. C. Kurtz ◽  
W. T. Sledd
Keyword(s):  
Banach Space ◽  
Power Series ◽  
Normal Matrix ◽  
Cesàro Means ◽  
Summability Factors ◽  
Cesaro Means ◽  
Space Topology ◽  
Nörlund Means ◽  
Summability Field ◽  
Cesáro Means

AbstractIt is shown that for the Cesàro means (C, α) with α > - 1, and for a certain class of more general Nörlund means, summability of the series σan implies uniform summability of the series σan zn in a Stolz angle at z = 1.If B is a normal matrix and (B) denotes the series summability field with the usual Banach space topology, then the vectors {ek} (ek = {0,0,..., 1,0,...}) are said to form a Toplitz basis for (B) relative to a method H if H — Σakek = a for each a = {ak}ε(B). It is shown for example that the above relation holds for B = (C,α), α> − 1 , and H = Abel method; also for B = (C,α) and H = (C,β) with 0 ≤ α ≤ β.Applications are made to theorems on summability factors.

scholarly journals The elastic equilibrium of isotropic plates and cylinders

1949 ◽  
Vol 195 (1043) ◽  
pp. 533-552 ◽  
Keyword(s):  
Fourier Series ◽  
General Solution ◽  
Power Series ◽  
Elastic Equilibrium ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Isotropic Plates ◽  
First Approximation ◽  
Stress Components ◽  
Normal And Shear Stresses

A general solution of the elastic equations is obtained for problems of stress distributions in plates or cylinders when the bounding faces of the plates Z = ± h , or the flat ends of the cylinders, are free from applied normal and shear stresses. The solution is expressed either in the form of Fourier series in the co-ordinate Z , or in power series in Z , the coefficients of the series being certain functions of the x and y co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planes Z = ± h . The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variable z = x + iy . A first approximation to the part of the theory which deals with the bending of the plate yields a theory similar in character to that given recently by Reissner.

scholarly journals On (J, pn)-summability of Fourier series

1972 ◽  
Vol 18 (1) ◽  
pp. 13-17
Author(s):  
F. M. Khan
Keyword(s):  
Fourier Series ◽  
Power Series ◽  
Radius Of Convergence ◽  
Partial Sums ◽  
Summability Of Fourier Series ◽  
Image Position

Let pn>0 be such that pn diverges, and the radius of convergence of the power seriesis 1. Given any series σan with partial sums sn, we shall use the notationand

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