Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
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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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Convergence of orbital integrals on unitary groups in positive characteristic
Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
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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.