In this paper, we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extending 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.
Segal-Bargmann-Fock modules of monogenic functions
Sabadini, Irene;
2017-01-01
Abstract
In this paper, we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extending 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.File in questo prodotto:
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