84 research outputs found
On a Watson-like Uniqueness Theorem and Gevrey Expansions
We present a maximal class of analytic functions, elements of which are in
one-to-one correspondence with their asymptotic expansions. In recent decades
it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.),
that the formal power series solutions of a wide range of systems of ordinary
(even non-linear) analytic differential equations are in fact the Gevrey
expansions for the regular solutions. Watson's uniqueness theorem belongs to
the foundations of this new theory. This paper contains a discussion of an
extension of Watson's uniqueness theorem for classes of functions which admit a
Gevrey expansion in angular regions of the complex plane with opening less than
or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We
present conditions which ensure uniqueness and which suggest an extension of
Watson's representation theorem. These results may be applied for solutions of
certain classes of differential equations to obtain the best accuracy estimate
for the deviation of a solution from a finite sum of the corresponding Gevrey
expansion.Comment: 18 pages, 4 figure
Totally disconnected sets, Jordan curves, and conformal maps
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43186/1/10998_2005_Article_BF02018646.pd
Magnetically Oriented Bicelles with Monoalkylphosphocholines: Versatile Membrane Mimetics for Nuclear Magnetic Resonance Applications
On theorems of Jackson and Bernstein type in the complex plane
We consider best polynomial approximation to functions analytic in a Jordan domain D and continuous on . We relate theorems of Jackson and Bernstein type to the Hölder continuity of the exterior conformal mapping functions for D .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41343/1/365_2005_Article_BF02075464.pd
Confinement, phase transitions and non-locality in the entanglement entropy
In this paper we study the conjectural relation between confinement in a
quantum field theory and the presence of a phase transition in its
corresponding entanglement entropy. We determine the sufficient conditions for
the latter and compare to the conditions for having a confining Wilson line. We
demonstrate the relation in several examples. Superficially, it may seem that
certain confining field theories with a non-local high energy behaviour, like
the dual of D5 branes wrapping a two-cycle, do not admit the corresponding
phase transition. However, upon closer inspection we find that, through the
introduction of a regulating UV-cutoff, new eight-surface configurations
appear, that satisfy the correct concavity condition and recover the phase
transition in the entanglement entropy. We show that a local-UV-completion to
the confining non-local theories has a similar effect to that of the
aforementioned cutoff.Comment: 64 pages. Lots of figure
Asymptotic representation of conformal maps of strip domains without boundary regularity
On the boundary smoothness of conformal mappings between domains with nonsmooth boundaries
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