Publicação
Spectral theory for the fractal Laplacian in the context of h-sets
| dc.contributor.author | Caetano, António M. | |
| dc.contributor.author | Lopes, Sofia | |
| dc.date.accessioned | 2026-01-12T17:10:49Z | |
| dc.date.available | 2026-01-12T17:10:49Z | |
| dc.date.issued | 2010-11-17 | |
| dc.description.abstract | An h-set is a nonempty compact subset of the Euclidean n-space which supports a finite Radon measure for which the measure of balls centered on the subset is essentially given by the image of their radius by a suitable function h. In most cases of interest such a subset has Lebesgue measure zero and has a fractal structure. Let ω be a bounded C∞ domain in \documentclass{article}\begin{document}$\mathbb R̂n $\end{document} with Γ ⊂ ω. Letwhere (-δ)-1 is the inverse of the Dirichlet Laplacian in ω and trΓ is, say, trace type operator. The operator B, acting in convenient function spaces in ω, is studied. Estimations for the eigenvalues of B are presented, and generally shown to be dependent on h, and the smoothness of the associated eigenfunctions is discussed. Some results on Besov spaces of generalised smoothness on \documentclass{article}\begin{document}${{\bb R}̂n} $\end{document} and on domains which were obtained in the course of this work are also presented, namely pointwise multipliers, the existence of a universal extension operator, interpolation with function parameter and mapping properties of the Dirichlet Laplacian. | eng |
| dc.description.sponsorship | The authors would like to thank Professor Hans Triebel for his valuable suggestions and for the fruitful discussions during the preparation of this paper. The second named author is supported by Fundação para a Ciência e a Tecnologia (FCT) and European Social Fund ˆin the scope of Community Support Framework III. This research was also partially supported by Unidade de Investigação Matematica e Aplicações of Universidade de Aveiro through Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) ˜of FCT, cofinanced by the European Community Fund (FEDER). | |
| dc.identifier.citation | Caetano A.M., Lopes S., Spectral theory for the fractal Laplacian in the context of h-sets (2011) Mathematische Nachrichten, 284 (1), pp. 5 - 38. DOI: 10.1002/mana.200910214 | |
| dc.identifier.doi | 10.1002/mana.200910214 | |
| dc.identifier.issn | 0025-584X | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/15302 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Wiley | |
| dc.relation.hasversion | https://onlinelibrary.wiley.com/doi/full/10.1002/mana.200910214?msockid=06f167facdc96ca237d0714ecc3a6daf | |
| dc.relation.ispartof | Mathematische Nachrichten | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Extension operator | |
| dc.subject | Fractals | |
| dc.subject | Function spaces | |
| dc.subject | h-sets | |
| dc.subject | Interpolation | |
| dc.subject | Laplacian | |
| dc.subject | Spectral theory | |
| dc.subject | Traces | |
| dc.title | Spectral theory for the fractal Laplacian in the context of h-sets | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 38 | |
| oaire.citation.issue | 1 | |
| oaire.citation.startPage | 5 | |
| oaire.citation.title | Mathematische Nachrichten | |
| oaire.citation.volume | 284 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 |