Article
Ufa Mathematical Journal
Volume 7, Number 4, pp. 154-165
About a conjecture regarding plurisubharmonic functions
Berdellima A.
DOI:10.13108/2015-7-4-154
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In this work we present Khabibullin's conjecture in its different equivalent forms. Applying the concept of the integral operator, we transform the original conjecture into a new form which proves to be helpful in studying it by means of the Laplace transform. Using Laplace transform of integral inequalities, we are able to show the uniqueness of a solution that satisfies both inequalities with identity. Furthermore we provide a new proof of Khabibullin's theorem by methods of the Laplace transform and contour integration from complex analysis. However, this method of transform fails to prove the conjecture and a brief reasoning is provided.