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- W3044283423 abstract "We establish effective elimination theorems for differential-difference equations. Specifically, we find a computable function $B(r,s)$ of the natural number parameters $r$ and $s$ so that for any system of algebraic differential-difference equations in the variables $mathbf{x} = x_1, ldots, x_q$ and $mathbf{y} = y_1, ldots, y_r$ each of which has order and degree in $mathbf{y}$ bounded by $s$ over a differential-difference field, there is a non-trivial consequence of this system involving just the $mathbf{x}$ variables if and only if such a consequence may be constructed algebraically by applying no more than $B(r,s)$ iterations of the basic difference and derivation operators to the equations in the system. We relate this finiteness theorem to the problem of finding solutions to such systems of differential-difference equations in rings of functions showing that a system of differential-difference equations over $mathbb{C}$ is algebraically consistent if and only if it has solutions in a certain ring of germs of meromorphic functions." @default.
- W3044283423 created "2020-07-29" @default.
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- W3044283423 date "2020-10-14" @default.
- W3044283423 modified "2023-10-16" @default.
- W3044283423 title "Elimination of unknowns for systems of algebraic differential-difference equations" @default.
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- W3044283423 doi "https://doi.org/10.1090/tran/8219" @default.
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