Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies [Comm. Pure Appl. Math., 41 (1988), pp

Abstract. We continue the study of constructing compactly supported orthonormal B-spline wavelets originated by T.N.T. Goodman. We simplify his constructive steps for compactly supported orthonormal scaling functions and provide an inductive method for constructing compactly supported orthonormal

We compute the compactly supported cohomology of the standard realization of any locally finite building.

properties: shearlet systems can be generated by one function, they provide precise resolution of wavefront sets, they allow compactly supported analyzing elements, they are associated with fast decomposition algorithms, and they provide a unified treatment of the continuum and the digital realm. The aim

[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 interpolationwith constructions of compactly supported solutions for cardinal interpolation to gain compactly supported fundamental

Abstract. Let • • • C K _ ] c Vq c Vx c • • • be a multiresolution analysis of L2 generated by the mth order 5-spline Nm{x). In this paper, we exhibit a compactly supported basic wavelet i//m(x) that generates the corresponding orthogonal complementary wavelet subspaces..., W _ \, Wo, Wx

This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions. It was shown in [D1] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the trivial case; and also shown in [L] and [GM

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In this paper, we consider the asymptotic regularity of Daubechies scaling functions and construct examples of M-band scaling functions which are both orthonormal and cardinal for M ¢ 3. � 1999 Academic Press Key Words: multiresolution; M-band scaling function; M-band wavelets; cardinal function; orthonormality. 1.

. We prove that a compactly supported spline function OE of degree k satisfies the scaling equation OE(x) = P N n=0 c(n)OE(mx \Gamma n) for some integer m 2, if and only if OE(x) = P n p(n)B k (x \Gamma n) where p(n) are the coefficients of a polynomial P (z) such that the roots of P (z