Segal–Bargmann transform for generalized partial-slice monogenic functions

Zhenghua Xu^a, I. Sabadini<sup>b

a</sup> School of Mathematics, Hefei University of Technology, Hefei, P. R. China
^b Politecnico di Milano, Dipartimento di Matematica, Milano, Italy

Аннотация: The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to develop the Segal–Bargmann transform and give a Schrödinger representation in the setting of generalized partial-slice monogenic functions. To this end, the generalized partial-slice Cauchy–Kovalevskaya extension plays a crucial role.

Ключевые слова: functions of a hypercomplex variable, monogenic functions, slice monogenic functions, Segal–Bargmann transform.

УДК: 517.443+517.53

MSC: Primary 30G35; Secondary 44A15, 30H20

Поступило в редакцию: 20.11.2024

Язык публикации: английский

DOI: 10.4213/im9671

 Англоязычная версия: Izvestiya: Mathematics, 2025, 89:6, 1182–1207

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