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- W3045302579 endingPage "2022" @default.
- W3045302579 startingPage "2006" @default.
- W3045302579 abstract "Regularized approaches have been successfully applied to linear system identification in recent years; many of them model unknown impulse responses exploiting the so-called Reproducing Kernel Hilbert Spaces (RKHSs) that enjoy the notable property of being in one-to-one correspondence with the class of positive semidefinite kernels. The necessary and sufficient condition for a RKHS to be stable, i.e., to contain only BIBO stable linear dynamic systems, has been known in the literature since at least 2006. However, an open question still persists and concerns the equivalence of such a condition with the absolute summability of the kernel. This paper provides a definite answer to this matter by proving that such correspondence does not hold. A counterexample is introduced that illustrates the existence of stable RKHSs that are induced by nonabsolutely summable kernels." @default.
- W3045302579 created "2020-07-29" @default.
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- W3045302579 date "2020-01-01" @default.
- W3045302579 modified "2023-10-10" @default.
- W3045302579 title "Kernel Absolute Summability Is Sufficient but Not Necessary for RKHS Stability" @default.
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- W3045302579 doi "https://doi.org/10.1137/19m1278442" @default.
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