Module-valued ODEs are defined via tensor products of Banach modules over finite-dimensional algebras, and the solution space of homogeneous linear cases is shown to be a finitely generated submodule.
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Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.
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Module-valued ordinary differential equations and structure of solution spaces
Module-valued ODEs are defined via tensor products of Banach modules over finite-dimensional algebras, and the solution space of homogeneous linear cases is shown to be a finitely generated submodule.
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Noncommutative differential geometry of ambiskew polynomial rings
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.