# Quick Question on Lp Space and Notation

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:

$L^1(ℝ)$ as in a function $g\in C^1(ℝ)\cap L^1(ℝ)$

$||u(\bullet ,t)||_{L^∞}$

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 $x\rightarrow\infty$ but that is incorrect.

## Answers and Replies

Dick
Science Advisor
Homework Helper
##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.

latex note

for what it is worth, the latex notation for the dot as in dot product is \cdot.

Thanks for the help guys!