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Matematicheskie Zametki, 1997, Volume 62, Issue 2, Pages 312–320
DOI: https://doi.org/10.4213/mzm1613
(Mi mzm1613)
 

Smooth regularization of plurisubharmonic functions

R. S. Yulmukhametov

Bashkir State University
References:
Abstract: We consider the problem of approximating a given plurisubharmonic function by smooth plurisubharmonic functions. We propose a new constructive approximation method that permits one to obtain more detailed information about the approximating functions. Thus a function $u\in\operatorname{PSH}(\mathbb C^n)$ having finite growth order can be approximated by smooth functions $v\in\operatorname{PSH}(\mathbb C^n)$ so that the difference $|v-u|$ has almost logarithmic growth (Theorem 2). It can also be approximated so that the difference $|v-u|$ has a power-law growth; in this case, however, power-law estimates on $|\operatorname{grad}v|$ appear (Theorem 3).
Received: 05.09.1995
English version:
Mathematical Notes, 1997, Volume 62, Issue 2, Pages 260–267
DOI: https://doi.org/10.1007/BF02355913
Bibliographic databases:
UDC: 517.576
Language: Russian
Citation: R. S. Yulmukhametov, “Smooth regularization of plurisubharmonic functions”, Mat. Zametki, 62:2 (1997), 312–320; Math. Notes, 62:2 (1997), 260–267
Citation in format AMSBIB
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\by R.~S.~Yulmukhametov
\paper Smooth regularization of plurisubharmonic functions
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 2
\pages 312--320
\mathnet{http://mi.mathnet.ru/mzm1613}
\crossref{https://doi.org/10.4213/mzm1613}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1619869}
\zmath{https://zbmath.org/?q=an:0919.31003}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 2
\pages 260--267
\crossref{https://doi.org/10.1007/BF02355913}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000071268600032}
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  • https://doi.org/10.4213/mzm1613
  • https://www.mathnet.ru/eng/mzm/v62/i2/p312
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