(a) the
approximation property if for every compact set K [[subset].bar] Y and for every neighbourhood O of zero in Y there exists a continuous finite-dimensional linear map L:Y [right arrow] Y such that L(y) - y [omega] O for every y [omega] K;
From the
approximation property (3.5) with r = q and t = l + 1, we easily obtain
namely, we have in mind the
approximation property, the Bohr property which served as definition (existence of the almost periods) and the Bochner property (the compactness of the family of translates).
ABSTRACT: A non-empty subset S of a valued field K is said to have the optimal
approximation property if every element in the field K has a closest approximation in S.
From the
approximation property of the L[degrees]-projection, we have
This latter equation holds if and only if X has the compact
approximation property (see [GS], Cor.
And finally, an MLP network with sufficient hidden neurons can satisfy the universal
approximation property [29].
Looking at recent results in the area of ergodic theory (the mathematical study of dynamical systems with an invariant measure) concerning the complexity of the problem of classification of ergodic measure preserving transformations up to conjugacy, the structure of the outer automorphism group of a countable measure preserving equivalence relation, ergodic theoretic characterizations with the Haagerup
approximation property, and cocycle superrigidity, the author of this monograph realized that these apparently diverse results can all be understood within a unified framework.
In the case of Whittaker operator, for functions with positive values, the newly obtained nonlinear sampling operator has essentially a better
approximation property than its linear counterpart.
al l991) do not have the universal
approximation property, but Ridged-Polynomial network (Y.Shin, et.