Geodesic
Spectral properties of weighted automorphisms in uniform algebras
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 288-293

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The parts of spectra of weighted automorphisms in uniform algebras are completely described. 
@article{ZNSL_1979_92_a22,
     author = {A. K. Kitover},
     title = {Spectral properties of weighted automorphisms in uniform algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {288--293},
     publisher = {mathdoc},
     volume = {92},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a22/}
}
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A. K. Kitover. Spectral properties of weighted automorphisms in uniform algebras. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 288-293. http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a22/