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Quick Question on Lp Space and Notation

  1. Sep 29, 2013 #1
    I have a homework problem discussing the heat equation, and I have two questions about notation that I could not figure out through google searching:

    [itex]L^1(ℝ)[/itex] as in a function [itex]g\in C^1(ℝ)\cap L^1(ℝ)[/itex]

    [itex]||u(\bullet ,t)||_{L^∞}[/itex]

    The bullet in the second expression is actually a single dot at that height, but I could not find the latex symbol for it. I initially thought it was a limit as [itex]x\rightarrow\infty[/itex] but that is incorrect.
     
  2. jcsd
  3. Sep 29, 2013 #2

    Dick

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    ##L^1## is the set of all functions f such that |f| has a finite integral. ##L^\infty## is the max norm. Since the dot is in the first position it's the max of |u(x,t)| over all x for a fixed t if u is continuous. If u is not continuous, it's the max possibly excluding a set of measure 0. If you are dealing with the heat equation you probably don't have to worry about the 'measure 0' thing.
     
  4. Sep 29, 2013 #3
    latex note

    for what it is worth, the latex notation for the dot as in dot product is \cdot.
     
  5. Sep 29, 2013 #4
    Thanks for the help guys!
     
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