Geodesic
Two-scale relations for analogs of basis splines of small degrees
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 319-323

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For generalized linear and parabolic $B$-splines with uniform knots constructed with the help of only one function $\varphi(x)$, conditions are found that guarantee the validity of two-scale relations for these splines.
Keywords: $B$-spline, uniform knots, two-scale relation. 
@article{TIMM_2011_17_3_a31,
     author = {V. T. Shevaldin},
     title = {Two-scale relations for analogs of basis splines of small degrees},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {319--323},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a31/}
}
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V. T. Shevaldin. Two-scale relations for analogs of basis splines of small degrees. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 319-323. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a31/