Slice regular Malmquist-Takenaka system in the quaternionic Hardy spaces
Margit Pap
TL;DR
This paper introduces a slice regular Malmquist-Takenaka system in quaternionic Hardy spaces, proving its completeness and orthonormality, and analyzing the associated projection operator.
Contribution
It develops a quaternionic analogue of the Malmquist-Takenaka system, establishing its fundamental properties in Hardy spaces of hypercomplex variables.
Findings
The system forms a complete orthonormal basis in quaternionic Hardy spaces.
Properties of the projection operator associated with the system are characterized.
The system enables series expansions and approximation in quaternionic function theory.
Abstract
A slice regular analogue of the Malmquist-Takenaka system is investigated. It is proved that they form a complete orthonormal system in the quaternionic Hardy spaces of the unit ball. The properties of associated projection operator are studied. Key Words and Phrases: Functions of hypercomplex variables, quaternionic Hardy spaces, series expansions, interpolation, approximation by rational functions, quaternionic Malmquist-Takenaka system
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Holomorphic and Operator Theory