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Segal-Bargmann-Fock modules of monogenic functions

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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.
Keywords
CLIFFORD ANALYSIS, TRANSFORM, EQUATION

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Citation

Please use this url to cite or link to this publication:

Chicago
Peña Peña, Dixan, Irene Sabadini, and Franciscus Sommen. 2017. “Segal-Bargmann-Fock Modules of Monogenic Functions.” Journal of Mathematical Physics 58 (10).
APA
Peña Peña, D., Sabadini, I., & Sommen, F. (2017). Segal-Bargmann-Fock modules of monogenic functions. JOURNAL OF MATHEMATICAL PHYSICS, 58(10).
Vancouver
1.
Peña Peña D, Sabadini I, Sommen F. Segal-Bargmann-Fock modules of monogenic functions. JOURNAL OF MATHEMATICAL PHYSICS. 1305 WALT WHITMAN RD, STE 300, MELVILLE, NY 11747-4501 USA: AMER INST PHYSICS; 2017;58(10).
MLA
Peña Peña, Dixan, Irene Sabadini, and Franciscus Sommen. “Segal-Bargmann-Fock Modules of Monogenic Functions.” JOURNAL OF MATHEMATICAL PHYSICS 58.10 (2017): n. pag. Print.
@article{8542059,
  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.},
  articleno    = {103507},
  author       = {Pe{\~n}a Pe{\~n}a, Dixan and Sabadini, Irene and Sommen, Franciscus},
  issn         = {0022-2488},
  journal      = {JOURNAL OF MATHEMATICAL PHYSICS},
  language     = {eng},
  number       = {10},
  pages        = {9},
  publisher    = {AMER INST PHYSICS},
  title        = {Segal-Bargmann-Fock modules of monogenic functions},
  url          = {http://dx.doi.org/10.1063/1.5008651},
  volume       = {58},
  year         = {2017},
}

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