Convergence of biorthogonal series of biharmonic eigenfunctions by the method of titchmarsh

1982 ◽  
Vol 78 (3) ◽  
pp. 223-274 ◽  
Author(s):  
D. D. Joseph ◽  
L. D. Sturges ◽  
W. H. Warner
Keyword(s):  
Biorthogonal Series

Stokes Flow in a Driven Sector by Two Different Methods

1980 ◽  
Vol 47 (3) ◽  
pp. 482-484 ◽  
Author(s):  
J. Sanders ◽  
V. O’Brien ◽  
D. D. Joseph
Keyword(s):  
Finite Difference ◽  
Series Expansion ◽  
Stokes Flow ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Mutual Support ◽  
Biorthogonal Series ◽  
Total Angle

A biorthogonal series expansion and a numerical finite-difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques. For this problem the method of biorthogonal series is faster, cheaper, and more accurate.

The consistency of cardinal series

1954 ◽  
Vol 50 (1) ◽  
pp. 139-142
Author(s):  
M. E. Noble
Keyword(s):  
Fourier Transform ◽  
Integral Function ◽  
Image Position ◽  
Biorthogonal Series

1. Whittaker (7), generalizing a result of Ferrar(3), showed that the cardinal series based on the positive and negative integers is consistent in the sense that, ifand an integral function f (x) is denned bythen provided 0 < λ > 1In this note I show that results of Paley- Wiener, Levinson and others on biorthogonal series can be made to yield a consistency theorem for cardinal series based on sequences λn, wherethat is, serieswhereWe use Fourier transform technique and need hypotheses, a little more restrictive than Whittaker's, which would reduce in the case .

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