344 reputation
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age 26
visits member for 3 years, 2 months
seen Oct 19 '13 at 10:03

Sep
16
awarded  Popular Question
Jul
2
awarded  Curious
May
17
awarded  Popular Question
May
10
revised Dirichlet eigenvalue problem on the Hilbert cube
Included the final destination.
May
9
asked Dirichlet eigenvalue problem on the Hilbert cube
May
8
comment Spectral Theorem for bounded compact, self-adjoint operators as corollary of Hilbert-Schmidt theorem
Thank you very much. My only confusion with what you wrote (apart from some problems with subscripts - easily done) is that I'm not sure why you've found $B$ like this. Don't we get an orthonormal basis for $H$ 'for free' from the Hilbert-Schmidt theorem? Indeed, the theorem says, "Then $H$ has an orthonormal basis $\left\{ v_{n}\right\} _{n\in\mathbb{N}}$ consisting of eigenvectors of $T$."
May
8
comment Spectral Theorem for bounded compact, self-adjoint operators as corollary of Hilbert-Schmidt theorem
I've updated my post with Debnath and Mikusinski's outline proof. I'm somewhat baffled by it.
May
8
revised Spectral Theorem for bounded compact, self-adjoint operators as corollary of Hilbert-Schmidt theorem
Added Debnath and Mikusinski's proof of the spectral theorem.
May
8
asked Spectral Theorem for bounded compact, self-adjoint operators as corollary of Hilbert-Schmidt theorem
May
6
comment A periodic Sturm-Liouville problem: Eigenvalues of the Laplacian in One Dimension
I understand that periodic solutions don't become unbounded; however, I don't understand why there is no periodic nontrivial solution. Am I missing something?
May
6
comment Quadratic Diophantine Equations
That's brilliant. Thank you very much.
May
6
asked A periodic Sturm-Liouville problem: Eigenvalues of the Laplacian in One Dimension
May
6
accepted Parabolic PDEs: Boundary conditions
May
6
asked Parabolic PDEs: Boundary conditions
May
6
accepted Spectral family property: $\lambda \geq M \Rightarrow E_{\lambda} = I$
May
6
asked Spectral family property: $\lambda \geq M \Rightarrow E_{\lambda} = I$
May
5
accepted Null spaces and projections
May
4
comment A proof for this series?
There's a nice proof here: proofwiki.org/wiki/Sum_of_Sequence_of_Squares/Proof_4
May
4
asked Null spaces and projections
May
3
accepted Residual spectrum is empty