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. 
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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/

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