Geodesic
The Legendre operator function
Izvestiya. Mathematics , Tome 65 (2001) no. 6, pp. 1073-1083

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We study the properties of the resolving operator of the Cauchy problem for an abstract Legendre equation with an unbounded linear operator $A$. We establish a relationship between this resolving operator and that of the Cauchy problem for an abstract Euler–Poisson–Darboux equation and prove the coincidence of the sets of operators $A$ for which the Cauchy problems for the Legendre and Euler–Poisson–Darboux equations are uniformly well posed. 
@article{IM2_2001_65_6_a0,
     author = {A. V. Glushak},
     title = {The {Legendre} operator function},
     journal = {Izvestiya. Mathematics },
     pages = {1073--1083},
     publisher = {mathdoc},
     volume = {65},
     number = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_6_a0/}
}
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A. V. Glushak. The Legendre operator function. Izvestiya. Mathematics , Tome 65 (2001) no. 6, pp. 1073-1083. http://geodesic.mathdoc.fr/item/IM2_2001_65_6_a0/