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CATEGORIES:Analysis seminar
SUMMARY:Convergence of Almost Periodic Fourier Series - An
drew Bailey (Birmingham)
DTSTART:20100228T160000Z
DTEND:20100228T170000Z
UID:TALK345AT
URL:/talk/index/345
DESCRIPTION:Almost periodic functions are well studied for the
ir applications in differential equations but surp
risingly little work has been done in considering
some of the classical questions in Fourier analysi
s in this broader context. In particular\, many na
tural questions relating to convergence of almost
periodic Fourier series have not yet been answered
.\n\nThe principal difficulty working with almost
periodic functions is that many of the "standard t
ools" of Fourier analysis have either not been ada
pted or fail to work completely. This talk will ma
inly be focussed on showing that a certain maximal
operator bound in the Stepanov almost periodic fu
nction spaces implies almost everywhere convergenc
e of dyadic partial sums of almost periodic Fourie
r series. Along the way\, some of the adaptations
of "standard tools" will be highlighted and attent
ion will be drawn to some of places where they see
mingly cannot be adapted.\n\nTime permitting\, the
talk will conclude with some discussion of ongoin
g research into an almost periodic version of Carl
eson's famous theorem asserting almost everywhere
convergence of (regular partial sums of) Fourier s
eries.
LOCATION:Watson Building\, LRA
CONTACT:Neal Bez
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