1,373 reputation
415
bio website mathtm.blogspot.com
location University of California Los Angeles, CA
age
visits member for 2 years, 4 months
seen 2 hours ago

I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


Sep
22
answered When to use $\mathbf{P}$ , and when to use $\mathbb{P}$ as the symbol for probability?
Aug
30
awarded  Popular Question
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
22
comment Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
For the example sequence of continuous functions of $L1$ norm $1$ we have $|\phi(f_{n})|\to\infty$ as $n\to\infty$ by construction of the Dirac functions outlined above. Do you see this at least? Therefore, since $||\phi||\geq|\phi(f_{n})|$ for all $n$, the claim follows.
Jun
22
comment Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
I'm not sure why you're being asked such a question if you don't follow (b). Dirac functions to which I am referring are nonnegative bump functions that spike near the origin and approach 0 elsewhere (rapidly), but such that their total integral is always $1$. In particular, they belong to the class of functions you must consider in evaluating the $\sup$ appearing in the definiton of $||\phi||$.
Jun
22
awarded  Citizen Patrol
Jun
22
comment Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
If you followed hint you would quickly see $||\phi||=\infty$ since the example sequence of sample norms in the hint is unbounded.
Jun
22
comment Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
See my edit for (a). I made a slight oversight and you are correct about your comment.
Jun
22
revised Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
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Jun
22
revised Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
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Jun
22
answered Computing the norm of operator when space is equipped with sup norm and $L^1$ norm
Jun
22
answered Local minimal about x=0
Jun
6
comment (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
Thanks Saz! I'll have to check this textbook out. You make a lot of references to it in your answers.
Jun
6
accepted (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
Jun
6
revised Function defined by an integral.
added 293 characters in body
Jun
6
answered Function defined by an integral.
Jun
5
revised (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
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Jun
5
revised (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
added 194 characters in body
Jun
5
revised (Ito lemma proof): convergence of $\sum_{i=0}^{n-1}f(W(t_{i}))(W(t_{i+1})-W(t_{i}))^{2}.$
added 194 characters in body