This book defines and examines the counterpart of Schur functions
and Schur analysis in the slice hyperholomorphic setting. It is
organized into three parts: the first introduces readers to
classical Schur analysis, while the second offers background
material on quaternions, slice hyperholomorphic functions, and
quaternionic functional analysis. The third part represents the
core of the book and explores quaternionic Schur analysis and its
various applications. The book includes previously unpublished
results and provides the basis for new directions of research.
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