13,262 research outputs found
The Neumann Problem and Helmholtz Decomposition in Convex Domains
We show that the Neumann problem for Laplace's equation in a convex domain
with boundary data in is uniquely solvable for
. As a consequence, we obtain the Helmholtz decomposition of vector
fields in .Comment: 17 page
Spectral representation of infimum of bounded quantum observables
In 2006, Gudder introduced a logic order on bounded quantum observable set
. In 2007, Pulmannova and Vincekova proved that for each subset
of , the infimum of exists with respect to this logic order. In
this paper, we present the spectral representation for the infimum of
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