Volumes of unit balls of mixed sequence spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10370806" target="_blank" >RIV/00216208:11320/17:10370806 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201500414" target="_blank" >http://dx.doi.org/10.1002/mana.201500414</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201500414" target="_blank" >10.1002/mana.201500414</a>

Result language
angličtina
Original language name
Volumes of unit balls of mixed sequence spaces
Original language description
The volume of the unit ball of the Lebesgue sequence space l(p)(m) is very well known since the times of Dirichlet. We calculate the volume of the unit ball of the mixed norm l(q)(n) (l(p)(m)), whose special cases are nowadays popular in machine learning under the name of group Lasso. We give two proofs of the main results, one in the spirit of Dirichlet, the other one using polarization identities. The result is given by a closed formula involving the gamma function, only slightly more complicated than the one of Dirichlet. We consider the real as well as the complex case. We also consider the anisotropic unit balls. We close by an overview of open problems. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LL1203" target="_blank" >LL1203: Properties of functions and mappings in Sobolev spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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