Interpolation of operators
Approximation by superposition of sigmoidal and radial basis functions
Advances in Applied Mathematics
Fundamentality of ridge functions
Journal of Approximation Theory
TDI-subspaces of CRd and some density problems from neural networks
Journal of Approximation Theory
Discrete Applied Mathematics - Special issue: Vapnik-Chervonenkis dimension
Approximation by ridge functions and neural networks
SIAM Journal on Mathematical Analysis
Regular Article: Identifying Linear Combinations of Ridge Functions
Advances in Applied Mathematics
On best approximation by ridge functions
Journal of Approximation Theory
On the approximation of functional classes equipped with a uniform measure using ridge functions
Journal of Approximation Theory
Neural networks for optimal approximation of smooth and analytic functions
Neural Computation
Essential rate for approximation by spherical neural networks
Neural Networks
Multivariate approximation by translates of the Korobov function on Smolyak grids
Journal of Complexity
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We investigate the radial manifolds Rn, generated by a linear combination of n radial functions on Rd. We consider the best approximation of function classes by the manifold Rn. In particular, we prove that the deviation of the manifold Rn from the Sobolev class W2r,d in the Hilbert space L2 behaves asymptotically as n-r/d-1. We show the connection between the manifold Rn and the space of algebraic polynomials Pd,s of degree s. Namely, we prove there exist constants c1 and c2 such that the space Pd,s is either contained or not in Rn as n ≥ c1sd-1 or n ≤ c2sd-1, respectively.