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The Generalized Discrete Legendre Transformation

✍ Scribed by J.M.R Méndez-Pérez; G.Miquel Morales

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
242 KB
Volume
218
Category
Article
ISSN
0022-247X

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✦ Synopsis

The discrete transformation LF x s f x s Ý 2n q 1 r2 P x F n , ns0 n

Ž . where the P x 's denote the well-known Legendre polynomials, is an isomorphism n Ž . between the space L ‫ގ‬ of the complex-valued sequences of rapid descent and 0

Ž

. the space L L y1, 1 of all infinitely differentiable complex-valued functions defined on y1x -1, of slow growth in the end points y1 and 1. This result is extended to the corresponding dual spaces. A space of multipliers for these spaces is considered and the translation operator and the convolution are investigated on them. The operational calculus generated involves certain finite-difference operators and is applied to find the solution of some ordinary and partial finitedifference equations.

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