Wavelets of Multiplicity r

Construction of wavelets with multiplicity

Riassunto: Sia X un sottoinsieme di r elementi di uno spazio di Hilbert H e sia V0 il sottospazio chiuso generato dall’iterazione di X mediante l’operatore unitario U = (U1, . . . , Ud). Analogamente sia V1 ⊃ V0 il sottospazio generato da un insieme Y con s > r elementi. Si descrivono alcuni metodi per costruire un insieme Γ con s − r elementi che generi in modo simile il complemento ortogonale...

SPECTRAL MULTIPLICITY FOR Gln(R)

We study the behavior of the cuspidal spectrum of T\^, where %? is associated to Gln(i?) and V is cofinite but not compact. By a technique that modifies the Lax-Phillips technique and uses ideas from wave equation techniques, if r is the dimension of JP, Na{k) is the counting function for the Laplacian attached to a Hilbert space Ha, Ma(X) is the multiplicity function, and Ho is the space of cu...

Balanced Multi-wavelets in R

The notion of K-balancing was introduced a few years ago as a condition for the construction of orthonormal scaling function vectors and multi-wavelets to ensure the property of preservation/annihilation of scalarvalued discrete polynomial data of order K (or degree K − 1), when decomposed by the corresponding matrix-valued low-pass/high-pass filters. While this condition is indeed precise, to ...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Arbitrarily Smooth Orthogonal Nonseparable Wavelets in R

For each r ∈ N, we construct a family of bivariate orthogonal wavelets with compact support that are nonseparable and have vanishing moments of order r or less. The starting point of the construction is a scaling function that satisfies a dilation equation with special coefficients and a special dilation matrix M : the coefficients are aligned along two adjacent rows, and |det(M)| = 2. We prove...