A counterexample to the existence of a local plurisubharmonic peak function at infinity

We give an example of an unbounded pseudoconvex Reinhardt domain in , which is Kobayashi complete but admits no local plurisubharmonic peak function at infinity.

     

A counterexample to the existence of peaking functions

We construct a smoothly bounded pseudoconvex domain whose boundary contains no complex analytic variety such that some boundary point admits no holomorphic peak function.

     

A class of maximal plurisubharmonic functions

In this note, we introduce a class of maximal plurisubharmonic functions and use that class to prove some properties of maximal plurisubharmonics functions.     

Approximation of plurisubharmonic functions

We extend a result by Fornaæss and Wiegerinck [Ark. Mat. 1989;27:257–272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.     

A remark on the approximation of plurisubharmonic functions

We show by an example that the Demailly approximation sequence of a plurisubharmonic function, constructed via Bergman kernels, is not a decreasing sequence in general.     

Characterizations of plurisubharmonic functions

Science China Mathematics - We give characterizations of (quasi-)plurisubharmonic functions in terms of Lp-estimates of $overline{partial}$ and Lp-extensions of holomorphic functions.     

A local integral representation of strictly plurisubharmonic functions

Translated from Matematicheskie Zametki, Vol. 53, No. 6, pp. 108–115, June, 1993.     

Smooth regularization of plurisubharmonic functions

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 functionu ∈ PSH(ℂ ⁿ ) having finite growth order can be approximated by smooth functionsv ∈ PSH(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 |gradv| appear (Theorem 3). Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 312–320, August, 1997. Translated by I. P. Zvyagin     

Extension of functions to plurisubharmonic functions in a topological vector space

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 11, pp. 1443–1449, November, 1989.     

A counterexample for approximable functions

Let be the unit disk. We show that for some relatively closed set there is a function that can be uniformly approximated on by functions of , but such that cannot be written as , with and uniformly continuous on . This answers a question of Stray.