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

    Download PDF
    Article on MathNet

    Abstact


    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.