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Reproducing Kernel Hilbert Spaces in Probability and Statistics
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TLDR
Sobolev spaces as mentioned in this paper are weak-derivative or derivative in the sense of distributions, and they can be used to describe Fourier transform functions as well as generalized functions.Abstract:
1 Theory.- 2 RKHS AND STOCHASTIC PROCESSES.- 3 Nonparametric Curve Estimation.- 4 Measures And Random Measures.- 5 Miscellaneous Applications.- 6 Computational Aspects.- 7 A Collection of Examples.- to Sobolev spaces.- A.l Schwartz-distributions or generalized functions.- A.1.1 Spaces and their topology.- A.1.2 Weak-derivative or derivative in the sense of distributions.- A.1.3 Facts about Fourier transforms.- A.2 Sobolev spaces.- A.2.1 Absolute continuity of functions of one variable.- A.2.2 Sobolev space with non negative integer exponent.- A.2.3 Sobolev space with real exponent.- A.2.4 Periodic Sobolev space.- A.3 Beppo-Levi spaces.read more
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