286 research outputs found
Surgery of spline-type and molecular frames
We prove a result about producing new frames for general spline-type spaces
by piecing together portions of known frames. Using spline-type spaces as
models for the range of certain integral transforms, we obtain results for
time-frequency decompositions and sampling.Comment: 34 pages. Corrected typo
Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
Let be the general, reduced Heisenberg group. Our main result
establishes the inverse-closedness of a class of integral operators acting on
, given by the off-diagonal decay of the kernel. As a
consequence of this result, we show that if , where
is the operator given by convolution with , , is
invertible in \B(L^{p}(\mathbb{H})), then
(\alpha_{1}I+S_{f})^{-1}=\alpha_{2}I+S_{g}g\in L^{1}_{v}(\mathbb{H})$.
We prove analogous results for twisted convolution operators and apply the
latter results to a class of Weyl pseudodifferential operators. We briefly
discuss relevance to mobile communications.Comment: This version corrects two mistakes and recognizes the work of other
authors related to a corollary of our main theore
Observers for linear time-varying systems
AbstractWe give characterizations and necessary and sufficient existence conditions for tracking and asymptotic observers for linear functions of the state of a linear finite-dimensional time-varying state space system. We specialize the results to affine parameter varying systems and bilinear control systems
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