A Sampling Principle Associated with Saitoh’s Fundamental Theory of Linear Transformations
A more general form of a sampling theorem due to Saitoh is given, to the effect that members of certain reproducing kernel Hilbert function spaces are recoverable from samples via a sampling series. This series can be viewed as a discrete form of reproducing equation. The ‘information loss error’ associated with this series expansion is discussed.
The sampling principle of Kramer is generalized in this context, and several examples are given where the kernels arise from polynomials of Meixner type.
KeywordsHilbert Space Orthogonal Basis Sampling Theorem Sampling Theory Reconstruction Function
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