BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Timothy McNicholl (Iowa State University)
DTSTART:20200923T000000Z
DTEND:20200923T010000Z
DTSTAMP:20260423T005732Z
UID:CTA/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/30/">Whi
 ch Lebesgue spaces are computably presentable?</a>\nby Timothy McNicholl (
 Iowa State University) as part of Computability theory and applications\n\
 n\nAbstract\nWe consider the following question: ``If there is a computabl
 y presentable $L^p$ space\, does it follow that $p$ is computable?”  The
  answer is of course `no’ since the 1-dimensional $L^p$ space is just th
 e field of scalars.  So\, we turn to non-trivial cases.  Namely\, assume t
 here is a computably presentable $L^p$ space whose dimension is at least $
 2$.  We prove $p$ is computable if the space is finite-dimensional or if $
 p \\geq 2$.  We then show that if $1 \\leq p < 2$\, and if $L^p[0\,1]$ is 
 computably presentable\, then $p$ is right-c.e..  Finally\, we show there 
 is no uniform solution of this problem even when given upper and lower bou
 nds on the exponent.  The proof of this result leads to some basic results
  on the effective theory of stable random variables.  Finally\, we conject
 ure that the answer to this question is `no’ and that right-c.e.-ness of
  the exponent is the best result possible.\n
LOCATION:https://researchseminars.org/talk/CTA/30/
END:VEVENT
END:VCALENDAR