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

Abstract: 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.

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

UDC: 517.443+517.53

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

Received: 20.11.2024

Language: English

DOI: 10.4213/im9671

 English version: Izvestiya: Mathematics, 2025, 89:6, 1182–1207

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