TY - JOUR

T1 - Splines of Variable Approximation Order and Their Wavelet Decompositions

AU - Dem’yanovich, Yu K.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We construct spline (finite element) spaces of variable approximation order and find necessary and sufficient conditions for pseudosmoothness of such splines. We study embedding of the spline spaces on embedded subdivisions and construct the corresponding wavelet decompositions. The constructions are based on the approximation relations defined on a cell subdivision of a differentiable manifold under the assumption that the multiplicity of the covering by supports of the coordinate functions is variable, which causes the variable approximation order. The spline spaces possess the adaptive approximation property. The notion of pseudosmoothness lead to new families of embedded spaces.

AB - We construct spline (finite element) spaces of variable approximation order and find necessary and sufficient conditions for pseudosmoothness of such splines. We study embedding of the spline spaces on embedded subdivisions and construct the corresponding wavelet decompositions. The constructions are based on the approximation relations defined on a cell subdivision of a differentiable manifold under the assumption that the multiplicity of the covering by supports of the coordinate functions is variable, which causes the variable approximation order. The spline spaces possess the adaptive approximation property. The notion of pseudosmoothness lead to new families of embedded spaces.

UR - http://www.scopus.com/inward/record.url?scp=85076788730&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04626-x

DO - 10.1007/s10958-019-04626-x

M3 - Article

AN - SCOPUS:85076788730

VL - 244

SP - 401

EP - 418

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -