Geodesic
Cauchy and Poisson formulas for polyanalytic functions and applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 15-26

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We obtain new Cauchy and Poisson integral formulas for polyanalytic functions. As an application, we establish mean value theorems for functions polyanalytic and real polyharmonic in a disk. We also give applications to sharp estimates of generalized maximum modulus principle type for associated functions, and, in particular, to estimates for rational functions (components) in the problem of singularity separation for polyrational functions.
Keywords: polyanalytic and polyrational functions, Cauchy and Poisson integral formulas, mean value theorems, generalized maximum modulus principle. 
@article{IVM_2016_1_a1,
     author = {V. I. Danchenko},
     title = {Cauchy and {Poisson} formulas for polyanalytic functions and applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--26},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_1_a1/}
}
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V. I. Danchenko. Cauchy and Poisson formulas for polyanalytic functions and applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 15-26. http://geodesic.mathdoc.fr/item/IVM_2016_1_a1/