A Note on Gaussian BV Function and Its Heat Semigroup Characterization

Authors

  • Xiaona Liu School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
  • Xiangyun Xie School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
  • Yu Liu School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

DOI:

https://doi.org/10.4208/jms.v54n3.21.02

Keywords:

Heat Semigroup, Gauss Space, Bounded Variation Function.

Abstract

In this note, we investigate the properties of Gaussian BV functions and give a heat semigroup characterization of BV functions in Gauss space. In particular, the latter is the nontrivial generalization of classical De Giorgi's heat kernel characterization of function of bounded variation on Euclidean space to the case of Gauss space.

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Published

2021-03-29

Issue

Vol. 54 No. 3 (2021)

Section

Articles