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arXiv · 1212.0360

Function theory of antilinear operators

Marko Huhtanen·Allan Perämäki
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Abstract

Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping theorems. These spectral mapping theorems are inclusive in general. Equality can be established in the self-adjoint case. The arising functions are shown to possess a biradial character. It is shown that to any given set of Jacobi parameters corresponds a biradial measure yielding these parameters in an iterative orthogonalization process in this function space, once equipped with the corresponding $L^2$ structure.

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Marko Huhtanen, Allan Perämäki. 2012-12-03. Function theory of antilinear operators. https://arxiv.org/abs/1212.0360

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