Dr. Bojana Purtic is a scholar in mathematical analysis at the Faculty of Mathematics, University of Belgrade, where she serves in the Department of Mathematical Analysis and conducts doctoral research in Theoretical Mathematics and Applications. Her research addresses fundamental problems in real and complex analysis, with notable contributions to the theory of harmonic and hyperbolic harmonic functions, invariant Laplacian equations, and geometric inequalities. Dr. Purti?’s work has been published in internationally recognized peer-reviewed journals, and she is an active participant in leading mathematical symposia.

Green function for operator Tα,β on Bn and integral representation of continuous functions:In this article, we have considered for α,β ∈ R general Poisson kernel Pα,β(x,ζ) = cβ (1 −|x|2)α |x −ζ|β ,x ∈ Bn,ζ ∈ Sn−1, and found that for differential operator Tα,βu(x) = (1 −|x|2)2?u(x) +2(2α−2−β +n)(1−|x|2)⟨x,∇u(x)⟩ +(β −2α)(2α−2−β+n)(1−|x|2)u(x)+4α(α−1−β +n)u(x), is fulfilled Tα,βPα,β(x,ζ) = 0, for all ζ ∈ Sn−1. After that, for α(α − 1 − β + n) < 0 we found Green functions Gk α,β, k = 1,2 and proved that function u ∈ C2(Bn,Rn) ∩ C(Bn,Rn) can be represented by integral using Green function and operator Tα,β in the following way u(x) = Tα,βu(y)Gk α,β(x,y)(1 − |y|2)−2α+β−ndV (y), Bn with additional condition 2α > β − n+1, which is generalisation of Theorem 1.1. from article [ 1].