Product property of global $P$-extremal functions


  • Nguyen Quang Dieu
  • Tang Van Long



In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J. 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. Bos and N. Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N. Levenberg and M. Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.


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How to Cite

Dieu, N. Q., & Long, T. V. (2021). Product property of global $P$-extremal functions. MATHEMATICA SCANDINAVICA, 127(3).