Geodesic
The Nevalinna-Pick problem with supplementary conditions
Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 569-578

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Methods used in the $L$-problem, generalized to apply to several intervals, are employed in finding criteria for the existence and uniqueness of Solutions of the Nevalinna-Pick problem (for the upper half-plane) under the supplementary conditions: the interpolating function is holomorphic, real, and of constant sign on given intervals on the real axis. 
@article{MZM_1968_4_5_a9,
     author = {A. A. Nudelman},
     title = {The {Nevalinna-Pick} problem with supplementary conditions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--578},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a9/}
}
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A. A. Nudelman. The Nevalinna-Pick problem with supplementary conditions. Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 569-578. http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a9/