Geodesic
On some properties of weighted Hilbert spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 410-421

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We describe the weighted Hilbert spaces $ L_{2,w}(\Omega) $ with positive weight functions $ w(x) $ which are summable on every bounded interval. We give sufficient condition for $ L_{2,w_1}(\Omega) $ space to be extension of $ L_{2,w_2}(\Omega) $ space. We also describe how to use given result in statistical probability density estimation.
Keywords: integrable function spaces, Hilbert spaces, weighted function spaces, second order splines, probability density function estimating. 
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     author = {Vladislav V. Branishti},
     title = {On some properties of weighted {Hilbert} spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {410--421},
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     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2017_10_4_a1/}
}
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Vladislav V. Branishti. On some properties of weighted Hilbert spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 410-421. http://geodesic.mathdoc.fr/item/JSFU_2017_10_4_a1/