In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

Simple improvements to an approach for robust semidefinite programming are proposed. The matrix dilation reformulation used as the core idea in a work by Oishi [5] is improved in terms of computational complexity by applying standard sum-of-squares methods, and by introducing less conservative uncertainty dependent parameterizations of the dilation matrix.

Given a d× d expansive dilation matrix D, a measurable set E ⊂ R d is called a Dt-dilation generator of Rd if Rd is tiled (modulo null sets) by the collection {(Dt)jE, j ∈ Z}. Our main goal in this paper is to prove certain results relating the support of the Fourier transform of functions generating a wavelet or orthonormal affine system associated with the dilation D to an arbitrary set E whi...

Characterizations of the stability and orthonormality of a multivariate matrix refinable function Φ with arbitrary matrix dilation M are provided in terms of the eigenvalue and 1-eigenvector properties of the restricted transition operator. Under mild conditions, it is shown that the approximation order of Φ is equivalent to the order of the vanishing moment conditions of the matrix refinement ...

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality, and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multiobjective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly, and is dealt with...

Scaling functions and orthogonal wavelets are created from the coeecients of a lowpass and highpass lter (in a two-band orthogonal lter bank). For \multiilters" those coeecients are matrices. This gives a new block structure for the lter bank, and leads to multiple scaling functions and wavelets. Geronimo, Hardin, and Massopust constructed two scaling functions that have extra properties not pr...

Wavelets with matrix dilation are studied. An explicit formula for masks providing vanishing moments is found. The class of interpolatory masks providing vanishing moments is also described. For an interpolatory mask, formulas for a dual mask which also provides vanishing moments of the same order and for wavelet masks are given explicitly. An example of construction of symmetric and antisymmet...