On an algebra connected with Toeplitz operators in radial tube domains

This article is a study of an algebra acting in $L_2^m(\mathbf R^n)$ and obtained by extending the classical algebra of multidimensional singular integral operators with the help of the orthogonal projection $P=F^{-1}\chi(\xi)F$, where $\chi(\xi)$ is the characteristic function of some cone in $\mathbf R^n$, and $F$ and $F^{-1}$ are the direct and inverse Fourier transformations, respectively.
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