There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in ℝ . interpolation representations are called sampling theorems for band-limited signals signal analysis. The truncation, amplitude, jitter errors associated with the investigated ...

the date of receipt and acceptance should be inserted later] Summary. In this paper we combine an earlier method developed with K. Jetter on general cardinal interpolation with constructions of compactly supported solutions for cardinal interpolation to gain compactly supported fundamental solutions for the general interpolation problem. The general interpolation problem admits the interpolatio...

Let a and b be reals. We consider the compactly supported solutions φ :R→R of the twocoefficient dilation equation φ(x) = aφ(2x)+bφ(2x−1). In this paper, we determine sets Ba,b , Ca,b , and Za,b defined in the following way: let x ∈ [0,1]. We say that x ∈ Ba,b (resp., x ∈ Ca,b , x ∈ Za,b) if the zero function is the only compactly supported solution of the two-coefficient dilation equation, whi...

The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...

Let 1 p 1 and = (1 ; : : : ; r) T be a vector-valued compactly supported L p function on R d. Deene V p (() = n P r i=1 P j2Z d d i (j) i (? j) : (d i (j)) j2Z d 2 ` p ; 1 i r o : In this paper, we consider the p-frame property of the space V p (() with being compactly supported function in L p \ L p=(p?1). Moreover, for the one-dimensional case, we show that if f i (? j) : 1 i r; j 2 Zg is a p...