@article{Dieu_Long_2021, title={Product property of global $P$-extremal functions}, volume={127}, url={https://www.mscand.dk/article/view/129007}, DOI={10.7146/math.scand.a-129007}, abstractNote={<p>In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J.&nbsp;Siciak in Ann. Polon. Math., 39 (1981), 175–211. As a consequence, we obtain convexity for the sublevel sets of such extremal functions. Moreover, we also generalize the product property of $P$-extremal functions established by L.&nbsp;Bos and N.&nbsp;Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N.&nbsp;Levenberg and M.&nbsp;Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.</p>}, number={3}, journal={MATHEMATICA SCANDINAVICA}, author={Dieu, Nguyen Quang and Long, Tang Van}, year={2021}, month={Nov.} }