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arXiv · 1608.06790

Segal-Bargmann-Fock modules of monogenic functions

Dixan Peña Peña·Irene Sabadini·Franciscus Sommen
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Abstract

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.

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Dixan Peña Peña, Irene Sabadini, Franciscus Sommen. 2017-11-02. Segal-Bargmann-Fock modules of monogenic functions. https://doi.org/10.1063/1.5008651

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