Hilbert Spaces of Solutions to Polynomial Dirac Equations, Fourier Transforms and Reproducing Kernel Functions for Cylindrical Domains

2005 ◽  
pp. 611-636 ◽  
Author(s):  
Denis Constales ◽  
Soeren Krausshar
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Fourier Transforms ◽  
Kernel Functions ◽  
Dirac Equations ◽  
Cylindrical Domains

INDEFINITE KERNEL NETWORK WITH DEPENDENT SAMPLING

2013 ◽  
Vol 11 (05) ◽  
pp. 1350020 ◽  
Author(s):  
HONGWEI SUN ◽  
QIANG WU
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Function Class ◽  
Positive Definiteness ◽  
Reproducing Kernel Hilbert Spaces ◽  
Strong Mixing ◽  
Mixing Condition ◽  
Indefinite Kernel ◽  
Learning Rates ◽  
Kernel Hilbert Spaces

We study the asymptotical properties of indefinite kernel network with coefficient regularization and dependent sampling. The framework under investigation is different from classical kernel learning. Positive definiteness is not required by the kernel function and the samples are allowed to be weakly dependent with the dependence measured by a strong mixing condition. By a new kernel decomposition technique introduced in [27], two reproducing kernel Hilbert spaces and their associated kernel integral operators are used to characterize the properties and learnability of the hypothesis function class. Capacity independent error bounds and learning rates are deduced.

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