In this paper, we study Hankel operators in the quaternionic setting. In particular, we prove that they can be exploited to measure the L^\infty distance of a slice L^\infty function (i.e., an essentially bounded function on the quaternionic unit sphere that is affine with respect to quaternionic imaginary units) from the space of bounded slice regular functions (i.e., bounded quaternionic power series on the quaternionic unit ball). Among the difficulties arising from the non-commutative context, there is the lack of a good factorization result for slice regular functions in the Hardy space H^1
Quaternionic Hankel operators and approximation by slice regular functions / Sarfatti, Giulia. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 65:(2016), pp. 1735-1757. [10.1512/iumj.2016.65.5896]
Quaternionic Hankel operators and approximation by slice regular functions
SARFATTI, GIULIA
2016
Abstract
In this paper, we study Hankel operators in the quaternionic setting. In particular, we prove that they can be exploited to measure the L^\infty distance of a slice L^\infty function (i.e., an essentially bounded function on the quaternionic unit sphere that is affine with respect to quaternionic imaginary units) from the space of bounded slice regular functions (i.e., bounded quaternionic power series on the quaternionic unit ball). Among the difficulties arising from the non-commutative context, there is the lack of a good factorization result for slice regular functions in the Hardy space H^1File | Dimensione | Formato | |
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