Geodesic
Weighted substitution operators in spaces of analytic functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 154-161

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The spectrum of weighted conformal substitution operators is determined in a large class of Banach spaces of analytic functions, including many spaces whose norm is defined in terms of the properties of the functions themselves and of their derivatives. 
@article{ZNSL_1985_141_a8,
     author = {A. K. Kitover},
     title = {Weighted substitution operators in spaces of analytic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--161},
     publisher = {mathdoc},
     volume = {141},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a8/}
}
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A. K. Kitover. Weighted substitution operators in spaces of analytic functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 154-161. http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a8/