Abstract
In this paper we study spaces of functions on domains with a conical singularity, which arise naturally if we study hyperbolic and parabolic evolution equations on such domains. We state conditions under which these spaces are Banach algebras, a result which is of independent interest. As applications, we remark that this implies local existence of solutions of Cauchy problems for semilinear, hyperbolic and parabolic partial differential equations with zero Dirichlet boundary conditions and a power-nonlinearity.
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