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(18 citation statements)

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“…. , x N } that are Π d s -unisolvent and all vectors a ∈ R N that satisfy zero moment conditions on X in the sense of (8), that is λ a,X p = 0 for each p ∈ Π d s . We can define an inner product on these functionals by…”

confidence: 99%

“…. , x N } that are Π d s -unisolvent and all vectors a ∈ R N that satisfy zero moment conditions on X in the sense of (8), that is λ a,X p = 0 for each p ∈ Π d s . We can define an inner product on these functionals by…”

confidence: 99%

“…A few articles deal with the case Ω unbounded (Madych and Potter [12], Madych [11] and Arcangéli et al [3]). For a survey on sampling inequalities and their applications, the reader is referred to Rieger et al [17]. The purpose of this paper is to extend the results of [2] and [3], for both cases Ω bounded and Ω = R n , in two directions: to allow fractional order semi-norms on the left-hand side of the sampling inequality (1.1), and to admit derivative pointwise values on the second term of the right-hand side of (1.1), so increasing the order of the approximation parameter d.…”

mentioning

confidence: 99%

“…We now use the much more recent framework of sampling inequalities in reproducing kernel Hilbert spaces (see, e.g. [31]) to obtain the same error bounds as already reported in [42]. The following discussion closely follows [31,34] and also draws on some ingredients from [42].…”

confidence: 93%