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- W2230757501 abstract "Consider a function x defined on some interval of the real axis and taking values in ℂ n (we incorporate ℝn-valued functions by interpreting ℝn as the subspace of ℂn consisting of elements that have, for each component, a zero imaginary part). We are interested in situations where the variable on the real axis is interpreted as time, and therefore denoted by t, and where the derivative (dot x) of x at some time t depends linearly on the history of x that is, on values of x for times less than or equal to t. In this chapter we concentrate on time translation invariant (or, in other words, autonomous) problems, where only the values of x matter and not the time t itself. In addition we assume that (dot x)depends on a finite segment of the history only. More precisely, we postulate the existence of h > 0 such that (dot x)(t) may depend (linearly) on x(τ) for t — h ≤ τ ≤ t but not on x(τ) for τ t. Given these restrictions we would like to consider a general equation. However, some more choices have to be made before we can state precisely what is the “general” equation." @default.
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- W2230757501 date "1995-01-01" @default.
- W2230757501 modified "2023-09-23" @default.
- W2230757501 title "Linear autonomous RFDE" @default.
- W2230757501 doi "https://doi.org/10.1007/978-1-4612-4206-2_2" @default.
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