Segal-Bargmann transform for generalized partial-slice monogenic functions

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.

26 pages

References in corpus (7)

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• On the Bargmann-Fock-Fueter and Bergman-Fueter integral transforms
• Extending coherent state transforms to Clifford analysis
• Coherent State Transforms and the Weyl Equation in Clifford Analysis
• Generalized partial-slice monogenic functions
• On the Fueter-Sce theorem for generalized partial-slice monogenic functions
• The Cholewinski-Fock space in the Slice Hyperholomorphic Setting