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This chapter contains some grounds for the study of entire slice regular functions as well as a panorama on the available literature on the function theory of slice regular functions, their applications to a functional calculus, to Schur analysis and to the quaternionic spectral theory.
KeywordsEntire Function Bergman Space Clifford Algebra Functional Calculus Monogenic Function
The first two authors are grateful to Chapman University for the kind hospitality and the support during the periods in which this work has been written. The second author thanks the project FIRB 2012 “Geometria Differenziale e Teoria Geometrica delle Funzioni” for partially supporting this research.