# Strict deformation quantization of locally convex algebras and modules

September 27, 2011

In this work various symbol spaces with values in a sequentially complete
locally convex vector space are introduced and discussed. They are used to
define vector-valued oscillatory integrals which allow to extend Rieffel's
strict deformation quantization to the framework of sequentially complete
locally convex algebras and modules with separately continuous products and
module structures, making use of polynomially bounded actions of
$\mathbb{R}^n$. Several well-known integral formulas for star products are
shown to fit into this general setting, and a new class of examples involving
compactly supported $\mathbb{R}^n$-actions on $\mathbb{R}^n$ is constructed.

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