Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This...Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his (her) null emission coordinates from the emitters which provide him his (her) position and trajectory.展开更多
In this paper positive definite matrix functionals defined on a set of square integrable matrix valued functions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. ...In this paper positive definite matrix functionals defined on a set of square integrable matrix valued functions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. Riemann-Lebesgue matrix property and a Bessel-Parseval matrix inequality are given.展开更多
文摘Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his (her) null emission coordinates from the emitters which provide him his (her) position and trajectory.
文摘In this paper positive definite matrix functionals defined on a set of square integrable matrix valued functions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. Riemann-Lebesgue matrix property and a Bessel-Parseval matrix inequality are given.
