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Smooth regularization of plurisubharmonic functions
R. S. Yulmukhametov Bashkir State University
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
Citation:
R. S. Yulmukhametov, “Smooth regularization of plurisubharmonic functions”, Mat. Zametki, 62:2 (1997), 312–320; Math. Notes, 62:2 (1997), 260–267
Linking options:
https://www.mathnet.ru/eng/mzm1613https://doi.org/10.4213/mzm1613 https://www.mathnet.ru/eng/mzm/v62/i2/p312
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Abstract page: | 339 | Full-text PDF : | 190 | References: | 50 | First page: | 1 |
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