Discrete Variable Transformations on Symplectic Systems and Even Order Difference Operators
✍ Scribed by Tammy Voepel
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 212 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Change of independent variable t = 1/x motivates variable step size discretizations of even order differential operators. We develop variable change methods for discrete symplectic (i.e., J-orthogonal) systems. This enables us to perform simultaneous change of independent and dependent variables on discrete linear Hamiltonian systems and on newly defined even order variable step size formally self adjoint difference operators. These variable changes yield a new system which is related to the original system by an operator identity. We generalize results of Bohner and Došlý on transformations of formally self-adjoint scalar difference operators. They only considered a change of dependent variable whereas these methods allow y x n = µ x n z t n where t n = f x n These variable change results bring the subject of transformation theory for even order difference operators closer to the known transformation theory in the continuous case.