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Feb
7
awarded  Enlightened
Feb
7
awarded  Nice Answer
Feb
4
answered Derivative of improper integral.
Jan
29
awarded  Good Answer
Jan
28
comment Given a $C_c^∞(G)$-valued random variable, is $C_c^∞(G)∋φ↦\text E[\langle\xi,φ\rangle]$ an element of the dual space of $C_c^∞(G)$?
@0xbadf00d I think the general assumption is exactly that $E[\xi]$ exists and is a bounded functional. At least, this is what I'm seeing in Gelfand & Vilenkin and a couple books by Zabczyk. Most "standard" stochastic process (Gaussian, Poisson, etc) will satisfy this assumption. Something more exotic? I'm not sure.
Jan
27
answered Given a $C_c^∞(G)$-valued random variable, is $C_c^∞(G)∋φ↦\text E[\langle\xi,φ\rangle]$ an element of the dual space of $C_c^∞(G)$?
Jan
15
asked Reference request: correlation and spectral analysis of stochastic processes
Jan
2
comment Clarification on point spectrum of an operator
Oh wait, I didn't see that you had two different $T$'s. Your reasoning about $\lambda = 1$ seems correct for your second $T$.
Jan
2
comment Clarification on point spectrum of an operator
You're correct about $\lambda = 0$ not being an eigenvalue. Check your work for $\lambda = 1$, though. It doesn't satisfy $Tx = x$.
Jan
2
answered Why doesn't the dot product give you the coefficients of the linear combination?
Jan
2
comment Clarification on point spectrum of an operator
Edited, thanks.
Jan
2
revised Clarification on point spectrum of an operator
added 6 characters in body
Jan
2
answered Clarification on point spectrum of an operator
Dec
22
comment What is the matrix property, 'hollowness'?
A link/reference to the paper would be good.
Dec
16
answered Does invertible diagonalizable matrix have its inverted matrix diagonalizable?
Dec
16
comment Use the Cholesky Theorem to prove the equivalence of two properties of symmetric matrices
Not entire sure where you're stuck. 1 follows from 2 fairly easily, and if you're able to use the Cholesky factorization, 2 follows from the symmetry assumption and 1 by choosing the $x^{(i)}$ to be the columns of $L$.
Dec
7
comment Alternative to Arnold's mathematical methods
A good option is "The Variational Principles of Mechanics" by Lanczos. Plus it's a Dover book, so cheap.
Nov
30
comment A question about proving continuity using an epsilon-delta proof
A few things about this question are confusing. You want to prove that $f(x)$ is continuous at $c=2$...what is $c$? Did you mean $x=2$? And what is $V_1(2)$?
Nov
29
comment Legendre polynomial for $p_k(1)$
It's always a good idea to show some work. What have you tried?
Nov
29
answered Legendre polynomial for $p_k(1)$