Titel
Spectral subspaces of Sturm-Liouville operators and variable bandwidth
Autor*in
Mark Jason Celiz
Institute of Mathematics, University of the Philippines
Abstract
We study spectral subspaces of the Sturm-Liouville operator f↦−(pf′)′ on R, where p is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by 1/p. Using the spectral theory of Sturm-Liouville operators, we make the reproducing kernel of these spectral subspaces more explicit and compute it completely in certain cases. As a contribution to sampling theory, we then prove necessary density conditions for sampling and interpolation in these subspaces and determine the critical density that separates sets of stable sampling from sets of interpolation.
Stichwort
Paley-Wiener spaceReproducing kernel Hilbert spaceSamplingDensity conditionSturm-Liouville theorySpectral theory
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Journal of Mathematical Analysis and Applications
Band
535
Ausgabe
2
ISSN
0022-247X
Erscheinungsdatum
2024
Publication
Elsevier BV
Erscheinungsdatum
2024
Zugänglichkeit
Rechte
Rechteangabe
© 2024 The Author(s)
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