Geodesic
A class of functions on a disjoint collection of segments
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 172-184

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Let $E=\bigcup\limits^m_{k=1}S_k$, where $S_k$ are disjoint segments, and let $\{\alpha_k\}$ be a collection of positive numbers, $0\alpha_k1$. We describe a class of functions $f$ on $E$ that admit approximation by polynomials of degree $\le n$ with the rate $\frac1{n^{\alpha_k}}$ on $S_k$. 
@article{ZNSL_1999_262_a7,
     author = {K. G. Mezhevitch and N. A. Shirokov},
     title = {A class of functions on a disjoint collection of segments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {172--184},
     publisher = {mathdoc},
     volume = {262},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a7/}
}
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K. G. Mezhevitch; N. A. Shirokov. A class of functions on a disjoint collection of segments. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 172-184. http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a7/