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- W4200552679 abstract "Abstract In 1993, Alcantara-Bode showed ([2]) that Riemann Hypothesisholds if and only if the integral operator on the Hilbert space L2(0; 1)having the kernel function defined by the fractional part of (y/x), isinjective. Since then, the injectivity of the integral operator used inequivalent formulation of RH has not been addressed nor has beendissociated from RH.We provided in this paper methods for investigating the injectivityof linear bounded operators on separable Hilbert spaces using theirapproximations on dense families of subspaces.On the separable Hilbert space L2(0,1), an linear bounded operator(or its associated Hermitian), strict positive definite on a dense familyof including approximation subspaces in built on simple functions, isinjective if the rate of convergence of its sequence of injectivity pa-rameters on approximation subspaces is inferior bounded by a not nullconstant, that is the case with the Beurling - Alcantara-Bode integraloperator.We applied these methods to the integral operator used in RHequivalence proving its injectivity." @default.
- W4200552679 created "2021-12-31" @default.
- W4200552679 creator A5031169974 @default.
- W4200552679 date "2021-12-29" @default.
- W4200552679 modified "2023-10-16" @default.
- W4200552679 title "On Injectivity of an Integral Operator Connected to Riemann Hypothesis" @default.
- W4200552679 doi "https://doi.org/10.21203/rs.3.rs-1159792/v3" @default.
- W4200552679 hasPublicationYear "2021" @default.
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