Abstract
We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functions to be inner or outer.
References
[1] Alpay, D., Bolotnikov, V. , Colombo, F. , Sabadini, I., Self-mappings of the quaternionic unit ball: multiplier properties, the Schwarz-Pick inequality, and the Nevanlinna-Pick interpolation problem, Indiana Univ. Math. J.64 (2015) no. 1, 151–180.Search in Google Scholar
[2] Arcozzi, N. and Sarfatti, G., Invariant metrics for the quaternionic Hardy space, J. Geom. Anal.25 (2015) no. 3, 2028–2059.Search in Google Scholar
[3] Bénéteau, C., Khavinson, D., Liaw, C., Seco, D., and Sola, A. A., Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants, J. Lond. Math. Soc.94 (2016) no. 3, 726–746.10.1112/jlms/jdw057Search in Google Scholar
[4] Chalendar, I., Gorkin, P., and Partington, J. R., Inner functions and operator theory, North-West. Eur. J. Math.1 (2015) 7–22.Search in Google Scholar
[5] de Fabritiis, C., Gentili, G., and Sarfatti, G., Quaternionic Hardy spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci.18 (2018) no. 2, 697–733.Search in Google Scholar
[6] Della Rocchetta, C., Gentili, G., Sarfatti, G., A Bloch-Landau theorem for slice regular functions, in Advances in Hypercomplex Analysis, ed. by G. Gentili, I. Sabadini, M. V. Shapiro, F. Sommen, D. C. Struppa, Springer INdAM Series, Springer, Milan, 2013, pp. 55-74.10.1007/978-88-470-2445-8_4Search in Google Scholar
[7] Garnett, J. B., Bounded analytic functions, Academic Press Inc., 1981.Search in Google Scholar
[8] Gentili, G., Stoppato, C., and Struppa, D. C., Regular functions of a quaternionic variable, Springer Monographs in Mathematics, Springer, Heidelberg, 2013.10.1007/978-3-642-33871-7Search in Google Scholar
[9] Ghiloni, R. , Perotti, A., Slice regular functions on real alternative algebras, Adv. Math., 226 (2011) 1662-1691.Search in Google Scholar
[10] Jamison, J. E., Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Caley numbers, Thesis (Ph.D.)–University of Missouri - Rolla, ProQuest LLC, Ann Arbor, MI, 1970, 178 pp.Search in Google Scholar
[11] Monguzzi, A. and Sarfatti, G., Shift invariant subspaces of slice L2 functions, Ann. Acad. Sci. Fenn. Math.43 (2018) 1045–1061.10.5186/aasfm.2018.4366Search in Google Scholar
[12] Seco, D., A characterization of Dirichlet inner functions, Complex Anal Oper. Th., online first.Search in Google Scholar
[13] Stoppato, C., Regular Moebius transformations of the space of quaternions, Ann. Global Anal. Geom., 39 (2010) 387-401.Search in Google Scholar
[14] Tobar, F. A., Mandic D. P., Quaternion reproducing kernel Hilbert spaces: existence and uniqueness conditions, IEEE Trans. Inform. Theory, 60 (2014) no.9, 5736–5749.10.1109/TIT.2014.2333734Search in Google Scholar
© 2019 Alessandro Monguzzi et al., published by De Gruyter
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