@inbook{3b724b57a54b49a2ba6629cbcf7a1bde,

title = "Operator-valued slice hyperholomorphic functions",

abstract = "In this chapter we introduce slice hyperholomorphic functions with values in a quaternionic Banach space. As in the complex case, there are two equivalent notions, namely weak and strong slice hyperholomorphicity. In order to properly define a multiplication between slice hyperholomorphic functions, we give a third characterization in terms of the Cauchy–Riemann system. Operator-valued functions can be obtained by using the so-called S-functional calculus. This calculus is associated with the notions of S-spectrum and S-resolvent, which are introduced and studied. We also present some hyperholomorphic extension results and, finally, we study the Hilbert-space-valued quaternionic Hardy space of the ball and its backward-shift invariant subspaces.",

author = "Daniel Alpay and Fabrizio Colombo and Irene Sabadini",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-319-42514-6_7",

language = "English",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing",

pages = "165--194",

booktitle = "Operator Theory",

}