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Cauchy Functions for Dynamic Equations on a Measure Chain

✍ Scribed by Elvan Akın

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
135 KB
Volume
267
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider the nth-order linear dynamic equation Px t = n i=0 p i t x σ i t = 0, where p i t 0 ≤ i ≤ n, are real-valued functions defined on . We define the Cauchy function K t s for this dynamic equation, and then we prove a variation of constants formula. One of our main concerns is to see how the Cauchy function for an equation is related to the Cauchy functions for the factored parts of the operator P. Finally we consider the equation Px t = n i=0 p i x σ i t = 0, where each of the p i 's is a constant, and obtain a formula for the Cauchy function. For our main results we only consider the time scale such that every point in is isolated.  2002 Elsevier Science (USA)

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