Geodesic
Pointwise and locally uniform convergence of holomorphic and harmonic functions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 665-678 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Classification : 30E10, 31B05, 31D05, 35J15, 35J99
Keywords: Osgood's theorem; approximation; maximum principle; harmonic space; elliptic PDE's 
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     title = {Pointwise and locally uniform convergence of holomorphic and harmonic functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {665--678},
     year = {1999},
     volume = {40},
     number = {4},
     mrnumber = {1756543},
     zbl = {1009.31002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_4_a5/}
}
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Štěpničková, Libuše. Pointwise and locally uniform convergence of holomorphic and harmonic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 665-678. http://geodesic.mathdoc.fr/item/CMUC_1999_40_4_a5/