Given a Hilbert space and the generator A of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any g(−s) ∈ H∞ we show that there exists an inf nite-time admissible output operator g(A). If g is rational, then this operator is bounded, and equals the “normal” def nition of g(A). In particular, when g(s) = 1/(s + α), α ∈ C + 0 , then this admissible output operator...

We resolve a long-standing question on L completeness of the timescale (or wavelet) system generated by the Mexican hat function, when p ≥ 2. Our main result concerns frequency-scale systems generated by modulation and dilation of a single function. The mixed frame operator (analysis followed by synthesis) is shown to be bijective from L(R) to itself, for 1 ≤ q < ∞, so that the frequency-scale ...

We describe a computer program which facilitates the analysis of a series of C.T. scans made while a stereotaxic fram fixed to the patient. program has 2 modes of operation: The operator may select a region and determine the three-dimensional frame coordinate. The operator may select a set of frame coordinates and have the computer program display these at the appropriate sites on C.T. scans. I...

The consensus operator is used for cumulative belief fusion in subjective logic, and takes beliefs on binary frames of discernment as input. Coarsening to a binary state space is therefore needed in case the original frame is larger than binary. Coarsening causes information loss in general, and can lead to inconsistent results when applying the consensus operator. We presents a method for norm...

In this article, we show that a finite dimensional Hilbert space can have an infinite Bessel sequence, but a normalized Bessel sequence in a finite dimensional Hilbert space must be of finite length. A relation between the dimension of a given finite dimensional Hilbert space and the bound of any finite normalized tight frame for the underlying space is obtained. Also some properties of the fra...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

The totality of the operators which correspond to their inverses in an automorphism of an abelian group G obviously constitutes a subgroup of G. I t is well known that G cannot contain any characteristic operator besides the identity unless this operator is of order 2, and that it cannot contain more than one characteristic operator of this order. Hence it results that whenever G contains any c...