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From the point of view of physics, a good solution of exterior boundary value problem in consideration of local topographic effect should reasonably contain both long wavelength effect, which describes global behavior of the earth’s gravity field, and short wavelength one, which shows local details of the field. Starting in the present paper with theory of functional analysis, we confine Ourselves to the situation that the boundary restriction appears as a finite discrete form, and finally draw two conclusions: (ⅰ) any solutions using the so-called fictitious point-masses lack any possibility of becoming either the best approximations or the least norm approximations in case of any possible choices of inner product and norm, and (ⅱ) the so-called Riesz representer approximations generally exist in general Hilbert spaces, while the famous geodetic collocation is nothing else but a special kind of Riesz representer approximations in the so-called reproducing Hilbert space. The final formula of the solut
From the point of view of physics, a good solution of exterior boundary value problem in consideration of local topographic effect should reasonably contain both long wavelength effect, which describes global behavior of the earth’s gravity field, and short wavelength one, which shows local details of the field. Starting in the present paper with theory of functional analysis, we confine Ourselves to the situation that the the boundary restriction appears as a finite discrete form, and finally draw two conclusions: (i) any solutions using the so-called fictitious point- masses lack lack lack lack masses masses masses masses ㄧ masses masses lack masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses masses is nothing else but a special kind of Riesz representer approximations in the so-called reproducing Hilbert space. The final formula of the solut