Dilational interpolatory inequalities
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Hegland, Markus; Anderssen, Robert S.
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Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms and, thereby, associated scales of interpolatory inequalities. Using one-parameter families of index functions based on the dilations of given index functions, new classes of interpolatory inequalities, dilational interpolatory inequalities (DII), are constructed. They have ordinary Hilbert scales (OHS) interpolatory inequalities as special cases. They represent a precise and...[Show more]
dc.contributor.author | Hegland, Markus | |
---|---|---|
dc.contributor.author | Anderssen, Robert S. | |
dc.date.accessioned | 2015-12-22T00:40:15Z | |
dc.date.available | 2015-12-22T00:40:15Z | |
dc.identifier.issn | 0025-5718 | |
dc.identifier.uri | http://hdl.handle.net/1885/95163 | |
dc.description.abstract | Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms and, thereby, associated scales of interpolatory inequalities. Using one-parameter families of index functions based on the dilations of given index functions, new classes of interpolatory inequalities, dilational interpolatory inequalities (DII), are constructed. They have ordinary Hilbert scales (OHS) interpolatory inequalities as special cases. They represent a precise and concise subset of variable Hilbert scales interpolatory inequalities appropriate for deriving error estimates for peak sharpening deconvolution. Only for Gaussian and Lorentzian deconvolution do the DIIs take the standard form of OHS interpolatory inequalities. For other types of deconvolution, such as a Voigt, which is the convolution of a Gaussian with a Lorentzian, the DIIs yield a new class of interpolatory inequality. An analysis of deconvolution peak sharpening is used to illustrate the role of DIIs in deriving appropriate error estimates. | |
dc.description.sponsorship | They also wish to acknowledge the support of the Radon Institute of Computational and Applied Mathematics, where the initial draft of this paper was finalized. | |
dc.publisher | American Mathematical Society | |
dc.rights | © 2010 CSIRO, Mathematics, Informatics and Statistics. http://www.sherpa.ac.uk/romeo/issn/0025-5718/..."author can archive post-print (ie final draft post-refereeing). On author's personal website, institutional repository, open access repositories and arXiv" from SHERPA/RoMEO site (as at 23/12/15). | |
dc.source | Mathematics of Computation | |
dc.title | Dilational interpolatory inequalities | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.notes | First published in Mathematics of Computation in Volume 90, number 274, 2011, published by the American Mathematical Society. | |
local.identifier.citationvolume | 80 | |
dc.date.issued | 2011-04 | |
local.identifier.absfor | 010301 | |
local.identifier.ariespublication | f2965xPUB1180 | |
local.publisher.url | http://www.ams.org/journals/ | |
local.type.status | Accepted Version | |
local.contributor.affiliation | Hegland, Markus, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University | |
local.contributor.affiliation | Anderssen, Robert S, CSIRO Mathematical and Information Sciences, Australia | |
local.bibliographicCitation.issue | 274 | |
local.bibliographicCitation.startpage | 1019 | |
local.bibliographicCitation.lastpage | 1036 | |
local.identifier.doi | 10.1090/S0025-5718-2010-02431-7 | |
dc.date.updated | 2016-02-24T08:10:07Z | |
local.identifier.scopusID | 2-s2.0-78751639086 | |
local.identifier.thomsonID | 000288587600018 | |
Collections | ANU Research Publications |
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