We consider approximate relations in the form of a system of linear algebraic equations that yield B φ -splines. We construct Lagrange type splines of the first order and give examples of polynomial, trigonometric, hyperbolic, and exponential B φ -splines. We also construct a system of linear functionals biorthogonal to the B φ -splines and resolve an interpolation problem generated by this system. For refined nonuniform grids we establish an embedding of spaces of B φ -splines. The decomposition and reconstruction formulas are obtained. Bibliography: 20 titles.

Original languageEnglish
Pages (from-to)617-631
Number of pages15
JournalJournal of Mathematical Sciences
Volume156
Issue number4
DOIs
StatePublished - Jan 2009

    Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

ID: 13741809