In this thesis, it is proposed to examine the difference equation:(z-h) ∆-hW(z) = A(z)W(z)(1) where W(z) is a vector with two components,∆-hW(h) = W(z) – W(z-h)/h(2)Here, A(z) is a 2x2 matrix, whose elements admit factorial series representations:A (z) = R + Σ∞s=0 As+1S!/z(z+h) ••• (z+sh)(3)R and As+l are square matrices of order two and independent of z. We also assume that eigen values of R do not differ by an integer. We hope to show that if (3) converges in some half plane, then (1) will have a fundamental matris solution of the form: W(z) = S(z)ZR where S(z) is a 2x2 matrix, whose elements have convergent factorial representation in some half plane.
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/182719 |
| Date | 03 June 2011 |
| Creators | Kawash, Nawal |
| Contributors | Puttaswamy, T. K. |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | 18, [1] leaves ; 28 cm. |
| Source | Virtual Press |
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