The Cauchy-Schwarz inequality and the approximation property (3.

With the characteristic function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], this implies the pointwise estimate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and hence the best approximation property of [[PI].

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.

Since we do not require an

approximation property of these basis functions, the construction is only based on a reference element.

We show that the homogeneous

approximation property and the comparison theorem hold for arbitrary coherent frames.

h] are chosen to satisfy a certain compatibility condition known as discrete inf-sup condition together with a certain

approximation property, then it is well-known [15, 16], under a certain shape-regularity of [T.

The remaining terms can be treated using the Neumann

approximation property from Theorem 4.

h] must be rich enough to fulfill the

approximation property (2.

KAPPA] and interpolation theory in Sobolev-Slobodeckij spaces give the

approximation propertyThe weak

approximation property for the tentative prolongator is known to give a bound on the convergence factor of the two-level and even multilevel method.