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THE COMPARATIVE INDEX FOR CONJOINED BASES OF SYMPLECTIC DIFFERENCE SYSTEMS

    https://doi.org/10.1142/9789812770752_0014Cited by:11 (Source: Crossref)
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    Abstract:

    We present the new concept applied for the comparison of conjoined bases of symplectic difference systems. This concept is closely related to the concept of multiplicities of focal points introduced by W. Kratz. Thus, the comparative index μ(i) = μ1(i) + μ2(i) gives us possibility to describe the case when the image condition and the Riccati inequality for conjoined bases Yi, do not hold. In this work we prove the main properties of μ(i) and investigate connections between μ(i) and the number of focal points m(i).