3,277 research outputs found
Block-diagonalisation of matrices and operators
In this short note we deal with a constructive scheme to decompose a
continuous family of matrices asymptotically as into
blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also
discuss the extension of the scheme to matrix families depending upon
additional parameters and operators on Hilbert spaces.Comment: 8 page
Dispersive estimates for hyperbolic systems with time-dependent coefficients
This paper is devoted to the study of time-dependent hyperbolic systems and
the derivation of dispersive estimates for their solutions. It is based on a
diagonalisation of the full symbol within adapted symbol classes in order to
extract the essential information about representations of solutions. This is
combined with a multi-dimensional van der Corput lemma to derive dispersive
estimates.Comment: 35 page
Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems
Necessary and sufficient conditions for convexity and strong convexity,
respectively, of sublevel sets that are defined by finitely many real-valued
-maps are presented. A novel characterization of strongly convex sets
in terms of the so-called local quadratic support is proved. The results
concerning strong convexity are used to derive sufficient conditions for
attainable sets of continuous-time nonlinear systems to be strongly convex. An
application of these conditions is a novel method to over-approximate
attainable sets when strong convexity is present.Comment: 20 pages, 3 figure
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