Poly-analytic Functions and Representation Theory

We propose the Lie-algebraic interpretation of poly-analytic functions in L 2 ( C , d μ ) , with the Gaussian measure d μ , based on a flag structure formed by the representation spaces of the sl ( 2 ) -algebra realized by differential operators in z and z ¯ . Following the pattern of the one-dimens...

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Veröffentlicht in:	Complex analysis and operator theory 2021-10, Vol.15 (7), Article 110
Hauptverfasser:	Turbiner, Alexander V., Vasilevski, Nikolai
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Analytic functions Complex variables Differential equations Higher Dimensional Geometric Function Theory and Hypercomplex Analysis Lie groups Mathematical analysis Mathematics Mathematics and Statistics Operator Theory Operators (mathematics)
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