Kramer’s Sampling Theorem With Discontinuous Kernels
Copyright policy )Kramer’s Sampling Theorem With Discontinuous Kernels
In 1957 Kramer gives an algorithm for reconstructing a function given by an integral transform \(f(t)= \int_a^b F(x)K(x,t)dx\) where \(K(x,t)\) is continuous in \(x\) and entire in \(t\). This reconstruction is performed starting from the values of \(f\) at some points. The authors show that this sampling theorem holds also in the case of certain discontinuous kernels.
- Carlos III University of Madrid Spain
- University of Central Florida United States
sampling theorem, Shannon and Kramer sampling theorems, Sturm-Liouville theory, Coding theorems (Shannon theory), discontinuous Sturm-Liouville problems, Sturm-Liouville problems, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), reconstruction of function by interpolatary series, Interpolation in approximation theory
sampling theorem, Shannon and Kramer sampling theorems, Sturm-Liouville theory, Coding theorems (Shannon theory), discontinuous Sturm-Liouville problems, Sturm-Liouville problems, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), reconstruction of function by interpolatary series, Interpolation in approximation theory
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