A Paley–Wiener theorem for some eigenfunction expansions

2011 ◽  
Vol 2 (3-4) ◽  
Author(s):  
S. Thangavelu
Keyword(s):  
Eigenfunction Expansions ◽  
Wiener Theorem

scholarly journals Theorems of Chernoff and Ingham for certain eigenfunction expansions

2021 ◽  
Vol 386 ◽  
pp. 107815
Author(s):  
Pritam Ganguly ◽  
Sundaram Thangavelu
Keyword(s):  
Eigenfunction Expansions

scholarly journals Paley–Wiener theorem for the q-Bessel transform and associated q-sampling formula

2009 ◽  
Vol 27 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Lazhar Dhaouadi ◽  
Wafa Binous ◽  
Ahmed Fitouhi
Keyword(s):  
Sampling Formula ◽  
Wiener Theorem ◽  
Bessel Transform

Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

1999 ◽  
Author(s):  
Keh-Yang Lee ◽  
Anthony A. Renshaw
Keyword(s):  
Solution Technique ◽  
Distributed Parameter ◽  
Moving Mass ◽  
Eigenfunction Expansions ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Mass Problem ◽  
Linearly Independent ◽  
Large Numbers ◽  
Speed Accuracy

Abstract A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.

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