Aksoy, Ü.Begehr, H.Çelebi, A.Shupeyeva, B.2025-05-052025-05-0520251072-337410.1007/s10958-025-07646-y2-s2.0-105001069350https://doi.org/10.1007/s10958-025-07646-yhttps://hdl.handle.net/20.500.14411/10567The Schwarz and iterated Dirichlet boundary-value problems are reported on for the polyanalytic operator in certain plane domains having a harmonic Green function. Hybrid polyharmonic Green functions are reviewed upon which open a variety of boundary-value problems for the polyharmonic operator. This topic is far from being complete. The higher the order of the polyharmonic operator the richer is the theory of related hybrid Green functions: they are constructed by continued convoluting harmonic Green, Neumann, Robin functions also incorporating polyharmonic Green–Almansi functions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.eninfo:eu-repo/semantics/closedAccess30E2530G2031A1031A2535J40Admissible DomainCauchy–Schwarz–Pompeiu RepresentationDirichlet Boundary-Value ProblemGreen FunctionGreen–Almansi FunctionPolyanalytic OperatorPolyharmonic Boundary-Value ProblemPolyharmonic Hybrid Green FunctionRing DomainRiquier Boundary-Value ProblemSchwarz Boundary-Value ProblemArticleN/AQ42876867883