Geodesic
On uniform Lebesgue constants of local exponential splines with equidistant knots
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 261-272

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For a linear differential operator $\mathcal {L}_r$ of arbitrary order $r$ with constant coefficients and real pairwise different roots of the characteristic polynomial, we study Lebesgue constants (the norms of linear operators from $C$ to $C$) of local exponential splines corresponding to this operator with a uniform arrangement of knots; such splines were constructed by the authors in earlier papers. In particular, for the third-order operator $\mathcal {L}_3=D(D^2-\beta^2)$ ($\beta>0$), we find the exact values of Lebesgue constants for two types of local splines and compare these values with Lebesgue constants of exponential interpolation splines.
Mots-clés : Lebesgue constants
Keywords: exponential splines, linear differential operator. 
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     author = {E. V. Strelkova and V. T. Shevaldin},
     title = {On uniform {Lebesgue} constants of local exponential splines with equidistant knots},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {261--272},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a23/}
}
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E. V. Strelkova; V. T. Shevaldin. On uniform Lebesgue constants of local exponential splines with equidistant knots. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 261-272. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a23/