Volume 54, Issue 3
A Note on Gaussian BV Function and Its Heat Semigroup Characterization

Xiaona Liu, Xiangyun Xie & Yu Liu

J. Math. Study, 54 (2021), pp. 250-261.

Published online: 2021-03

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  • 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.

  • AMS Subject Headings

28B10, 28A33, 26B30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

luckyxiaona@163.com (Xiaona Liu)

xiexiangyun719@163.com (Xiangyun Xie)

ustbmathliuyu@ustb.edu.cn (Yu Liu)

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@Article{JMS-54-250, author = {Liu , XiaonaXie , Xiangyun and Liu , Yu}, title = {A Note on Gaussian BV Function and Its Heat Semigroup Characterization}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {3}, pages = {250--261}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n3.21.02}, url = {http://global-sci.org/intro/article_detail/jms/18734.html} }
TY - JOUR T1 - A Note on Gaussian BV Function and Its Heat Semigroup Characterization AU - Liu , Xiaona AU - Xie , Xiangyun AU - Liu , Yu JO - Journal of Mathematical Study VL - 3 SP - 250 EP - 261 PY - 2021 DA - 2021/03 SN - 54 DO - http://doi.org/10.4208/jms.v54n3.21.02 UR - https://global-sci.org/intro/article_detail/jms/18734.html KW - Heat Semigroup, Gauss Space, Bounded Variation Function. AB -

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.

XiaonaLiu, XiangyunXie & YuLiu. (2021). A Note on Gaussian BV Function and Its Heat Semigroup Characterization. Journal of Mathematical Study. 54 (3). 250-261. doi:10.4208/jms.v54n3.21.02
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