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Sep
12
revised Why is this Moebius equivalence true?
rolled back to a previous revision
Sep
12
revised Why is this Moebius equivalence true?
edited tags
Sep
12
reviewed Close For $n>4$ the only nontrivial subgroup of symmetric group of order $n$ is alternating group.
Sep
12
reviewed Close Why is multiplication commutative - intuitive explanation
Sep
12
reviewed Close Prove that every bounded sequence has a convergent subsequence.
Sep
12
answered $L^2$ boundedness of Calderon Zygmund operator
Sep
12
comment $L^2$ boundedness of Calderon Zygmund operator
Please include in your question the complete definition of $M_{r,s}$ and $T_{r,s}$. Whenever possible we vastly prefer questions to be self-contained. Google book excerpts are not guaranteed to work everywhere.
Sep
12
answered A cute little system of nonlinear PDEs
Sep
12
revised A cute little system of nonlinear PDEs
edited tags; edited tags
Sep
11
awarded  Nice Answer
Sep
10
revised Maximize the parts in which a large number can be decomposed in a limited time
added 207 characters in body
Sep
8
comment Schrödinger versus heat equations
@AlexM. regarding your first point, you are absolutely correct. I made a mistake (halfway through writing my brain switched from the improper integral $\int K$ to the absolute integral $\int |K|$). I've fixed it above. For your second: no. There are some known expressions for some specific $V$, but none in general.
Sep
8
revised Schrödinger versus heat equations
Sorry, used total integral in two different senses in the section so that the answer made no sense. Fixed.
Sep
5
awarded  Nice Answer
Sep
5
comment Eigenfunctions and spectrum of $T:H \to H^*$ where $H$ is a Hilbert space
You are incorrectly generalizing. Starting with the notion of the spectrum for continuous operators $T:X\to X$, you try to generalise the notion to continuous operators $T:X\to Y$, when in fact, as paul garrett answered you below, the correct generalisation is to $T:X\to X$ a densely-defined unbounded operator.
Sep
5
comment Eigenfunctions and spectrum of $T:H \to H^*$ where $H$ is a Hilbert space
"$H^{-1}$ is the Hilbert space dual to $H^1$"... Riesz representation theorem notwithstanding. (My point being that one can identify the two under the $L^2$ pairing, but one can also identify $H^*$ with $H$ using the $\langle,\rangle_H$ pairing. The $H^{-1}$ norm on $(H^1)^*$ is in fact not the natural one induced by the usual relation $\sup_{\|x\|_{H} = 1} |\varphi(x)|$.)
Sep
5
comment Reference request: Measure theory and/or manifolds
It depends on university, course of study, etc. In my experience they are often introduced as a third year (American) or second year (European) undergraduate class. Though I have seen earlier and alter.
Sep
5
comment Eigenfunctions and spectrum of $T:H \to H^*$ where $H$ is a Hilbert space
What do you mean by $H^*$? How do you interpret the notion of eigenvector when $T$ sends elements of a space $H$ to a different space? (Formally you have $Tv = \lambda v$, what does this even mean if $Tv$ and $\lambda v$ are not in the same space?)
Sep
5
comment Arbitrary union/intersection in $\sigma$-algebra
(Wiki hammered as it is a literal copy of Daniel Fischer's comment)
Sep
5
comment Reference request: Measure theory and/or manifolds
What do you mean by "when"?