Abstract:
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.
UDC:
517.5:519.2
Received: 14.02.2017 Received in revised form: 17.05.2017 Accepted: 10.08.2017
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