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Pizzetti and Cauchy formulae for higher dimensional surfaces : a distributional approach

Ali Guzmán Adán (UGent) and Franciscus Sommen (UGent)
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Abstract
In this paper, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First we illustrate a general distributional method for integration over manifolds in R^m defined by means of k equations phi(1)(x) = ... = phi(k)(x) = 0. Next, we apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds SO(m)/SO(m - k). Besides, a distributional interpretation of invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded (m - k)-dimensional smooth surface.
Keywords
Applied Mathematics, Analysis, Pizzetti formula, Cauchy theorem, Integration, Distributions, Manifolds, Dirac operator, SPACE

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MLA
Guzmán Adán, Ali, and Franciscus Sommen. “Pizzetti and Cauchy Formulae for Higher Dimensional Surfaces : A Distributional Approach.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 489, no. 1, 2020, doi:10.1016/j.jmaa.2020.124140.
APA
Guzmán Adán, A., & Sommen, F. (2020). Pizzetti and Cauchy formulae for higher dimensional surfaces : a distributional approach. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 489(1). https://doi.org/10.1016/j.jmaa.2020.124140
Chicago author-date
Guzmán Adán, Ali, and Franciscus Sommen. 2020. “Pizzetti and Cauchy Formulae for Higher Dimensional Surfaces : A Distributional Approach.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 489 (1). https://doi.org/10.1016/j.jmaa.2020.124140.
Chicago author-date (all authors)
Guzmán Adán, Ali, and Franciscus Sommen. 2020. “Pizzetti and Cauchy Formulae for Higher Dimensional Surfaces : A Distributional Approach.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 489 (1). doi:10.1016/j.jmaa.2020.124140.
Vancouver
1.
Guzmán Adán A, Sommen F. Pizzetti and Cauchy formulae for higher dimensional surfaces : a distributional approach. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2020;489(1).
IEEE
[1]
A. Guzmán Adán and F. Sommen, “Pizzetti and Cauchy formulae for higher dimensional surfaces : a distributional approach,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 489, no. 1, 2020.
@article{8663796,
  abstract     = {In this paper, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First we illustrate a general distributional method for integration over manifolds in R^m defined by means of k equations phi(1)(x) = ... = phi(k)(x) = 0. Next, we apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds SO(m)/SO(m - k). Besides, a distributional interpretation of invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded (m - k)-dimensional smooth surface.},
  articleno    = {124140},
  author       = {Guzmán Adán, Ali and Sommen, Franciscus},
  issn         = {0022-247X},
  journal      = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
  keywords     = {Applied Mathematics,Analysis,Pizzetti formula,Cauchy theorem,Integration,Distributions,Manifolds,Dirac operator,SPACE},
  language     = {eng},
  number       = {1},
  pages        = {25},
  title        = {Pizzetti and Cauchy formulae for higher dimensional surfaces : a distributional approach},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2020.124140},
  volume       = {489},
  year         = {2020},
}

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