Function theory of antilinear operators

2012/12/03 by Huhtanen, Marko, Perämäki, Allan
#33C47 #47A05 #47A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1212.0360

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 L² structure.

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