We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

The basic operations for combining real values in the frame of decision analysis are the Weighted Mean (WM) and the Ordered Weighted Averaging operator (OWA). The weighted mean allows the system to compute an aggregate value from the ones coming from several sources, taking into account the reliability of each information source. Alternatively, the OWA operator allows the user to weight the val...

The Schrödinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schrödinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle – the Schrödinger line bundle. This line bundle has trivializations indexed by inertial observers and is associa...

Preprint No. 1239, Department of Mathematics, University of Utrecht, May 2002. Submitted to SIAM J. Numer. Anal. In “Adaptive Wavelet Methods II Beyond the Elliptic case” of Cohen, Dahmen and DeVore ([CDD00]), an adaptive method has been developed for solving general operator equations. Using a Riesz basis of wavelet type for the energy space, the operator equation is transformed into an equiva...

Abstract We define a new notion of fiberwise linear differential operator on the total space vector bundle E . Our main result is that operators are equivalent to (polynomial) derivations an appropriate line over E ? {E^{\ast}} believe this might represent first step towards definition m...

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given positive operator $A\in\B(\h)$, and number $\lambda\in [0,1]$, seminorm ${\|\cdot\|}_{(A,\lambda)}$ is defined set $\B_{A^{1/2}}(\h)$ in $\B(\h)$ having an $A^{1/2}$-adjoint. The combination sesquilinear form ${\langle \cdot, \...

Charles D. Kochakian has had a long and distinguished career in the field of endocrine physiology. His most important work concerned the anabolic actions of steroids. While still a graduate student, Kochakian showed that the anabolic effects of male hormones could be quantitated by measuring the changes they caused in urinary nitrogen balance. He subsequently showed that this anabolic effect wa...