Alexander Robertson

Alexander Robertson 1896-1970.

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Friedmann-robertson-walker Cosmologies

Abstract. Electrodynamics for self-interacting scalar fields in spatially flat FriedmannRobertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to grav...

Robertson Intelligent States

Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In case of canonical observables this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelli...

Muriel Robertson, 1883-1973.

Robertson Type Theorems for Frames

We extend Robertson’s theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone’s theorem and the theory of spectral multiplicity to analyze wandering frame collections. Motivated by wavelet theory, we explicitly apply our results to the action of the integers given by translations on L(R). This yields a new functional anal...