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- Title
Embedded Spaces of Trigonometric Splines and Their Wavelet Expansion.
- Authors
Dem'yanovich, Yu. K.
- Abstract
With each infinite grid X: ⋯ < x −1 < x 0 < x 1 < ⋯ we associate the system of trigonometric splines $$\{ \mathfrak{T}_j^B \}$$ of class C 1(α, β), the linear space and the functionals g ( i) ∈ ( C 1(α, β))* with the biorthogonality property: $$\left\langle {g(i),\mathfrak{T}_j^B } \right\rangle = \delta _{i,j}$$ (here $$\alpha \mathop = \limits^{def} \lim _{j \to - \infty } x_j ,\quad \beta \mathop = \limits^{def} \lim _{j \to + \infty } x_j$$ ). For nested grids $$\bar X \subset X$$ , we show that the corresponding spaces $$T^B (\bar X)$$ are embedded in $$T^B (X)$$ and obtain decomposition and reconstruction formulas for the spline-wavelet expansion $$T^B (X) = T^B (\bar X)\dot + W$$ derived with the help of the system of functionals indicated above.
- Subjects
EMBEDDED computer systems; WAVELETS (Mathematics); HARMONIC analysis (Mathematics); TRIGONOMETRY; MATHEMATICS
- Publication
Mathematical Notes, 2005, Vol 78, Issue 5/6, p615
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0165-1