With each infinite grid X: ⋯ < x -1 < x 0 < x 1 < ⋯ we associate the system of trigonometric splines {T j B} of class C 1(α, β), the linear space T B (X) = def {ũ| ũ = ∑ j c jT j B c j ∞ ℝ 1}, and the functionals g (i) (C 1(α, β))*with the biorthogonality property: 〈g (i),T j B〈 = δ i,j (here α = def lim j→-∞ xj, β = def lim j→+infin;xj). For nested grids X̄ ⊂ X, we show that the corresponding spaces T B(X̄) are embedded in T B (X) and obtain decomposition and reconstruction formulas for the spline-wavelet expansion T B (X) = T B (X̄)+ . W derived with the help of the system of functionals indicated above.

Original languageEnglish
Pages (from-to)615-630
Number of pages16
JournalMathematical Notes
Volume78
Issue number5-6
DOIs
StatePublished - 1 Nov 2005

    Scopus subject areas

  • Mathematics(all)

    Research areas

  • Biorthogonal system of functionals, Decomposition and reconstruction formulas, Gauge relations for splines, Nested grids, Trigonometric spline, Wavelet expansion

ID: 49712707