A Short Nonstandard Proof of the Radon-Nikodym Theorem
Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided
math.LO↗
arXiv subjects
Takashi Matsunaga
Publications and source records attributed to Takashi Matsunaga.
A short nonstandard proof of the Spectral Theorem for unbounded self-adjoint operators
By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
math.SP↗
A short nonstandard proof of the Doob-Meyer and Dol{é}ans-Dade theorems
Using nonstandard analysis, a very short and elementary proof of the Doob-Meyer decomposition and the Dol{é}ans Dade theorems is provided.
math.LO↗
Schrödinger equations in constrained space with several initial constraints
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schrödinger equation for this system is obtained. These constraint conditions are now allowed to depend not only on the coordinates but also on the velocities. It is shown that the hermiticity for the observables of the system restricts the geometrical structure of our world.
hep-th↗