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Relations between functional norms of a non-negative function and its square root on the positive cone of Besov and Triebel-Lizorkin spaces
Narvik University College, 8505 Narvik, Norway.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2009 (English)In: Applications of Mathematics in Engineering and Economics: proceedings of the 35th International Conference, Sozopol, Bulgaria, 7 - 12 June 2009 / [ed] George Venkov; Ralitza Kovacheva; Vesela Pasheva, Melville, NY: American Institute of Physics (AIP), 2009, 3-15 p.Conference paper (Refereed)
Abstract [en]

In this communication we study in detail the relations between the smoothness of f and √f in the case when the smoothness of the univariate non-negative functions f is measured via Besov and Triebel-Lizorkin space scales. The results obtained can be considered also as embedding theorems for usual Besov and Triebel-Lizorkin spaces and their analogues in Hellinger metric. These results can be used in constrained approximation using wavelets, with applications to probability density estimation in speech recognition, non-negative non-parametric regression-function estimation in positron-emission tomography (PET) imaging, shape/order-preserving and/or one-sided approximation and many others.

Place, publisher, year, edition, pages
Melville, NY: American Institute of Physics (AIP), 2009. 3-15 p.
, A I P Conference Proceedings Series, ISSN 0094-243X ; 1184:1
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URN: urn:nbn:se:ltu:diva-31336DOI: 10.1063/1.3271637Local ID: 57ce9530-ee59-11de-bae5-000ea68e967bISBN: 0-7354-0750-9OAI: diva2:1004570
Applications of Mathematics in Engineering and Economics Conference : 07/06/2009 - 12/06/2009
Validerad; 2009; 20091221 (grip)Available from: 2016-09-30 Created: 2016-09-30Bibliographically approved

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