28 research outputs found
On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and obstructions to smoothness of ``null infinity''
Various works have suggested that the Bondi--Sachs--Penrose decay conditions
on the gravitational field at null infinity are not generally representative of
asymptotically flat space--times. We have made a detailed analysis of the
constraint equations for ``asymptotically hyperboloidal'' initial data and find
that log terms arise generically in asymptotic expansions. These terms are
absent in the corresponding Bondi--Sachs--Penrose expansions, and can be
related to explicit geometric quantities. We have nevertheless shown that there
exists a large class of ``non--generic'' solutions of the constraint equations,
the evolution of which leads to space--times satisfying the
Bondi--Sachs--Penrose smoothness conditions.Comment: 8 pages, revtex styl
On Fourier transforms of radial functions and distributions
We find a formula that relates the Fourier transform of a radial function on
with the Fourier transform of the same function defined on
. This formula enables one to explicitly calculate the
Fourier transform of any radial function in any dimension, provided one
knows the Fourier transform of the one-dimensional function and
the two-dimensional function . We prove analogous
results for radial tempered distributions.Comment: 12 page
Characteristic functional equations of polynomials and the morera-carleman theorem
Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43923/1/10_2005_Article_BF02188016.pd