# L. Xu

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bio website location United States age member for 1 year, 7 months seen Dec 11 at 12:28 profile views 55

I'm a graduate student studying math at Illinois Institute of Technology. My interest is in Functional Analysis, PDE, Probability, Stochastics. Also I learn something on Algebra.

 5 Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$ 3 To show that $J(u) = \frac{1}{2}\int_\Omega |\nabla u|^2 -\frac{1}{p+1}\int_\Omega |u|^{p+1}$ is not bounded above for $1 < p < 2^*-1$ 2 Not using stochasstic integral how to prove $E\int_0^T W^2(t)dt<+\infty$? 2 Limit of quotient sequence 2 Show $f_n \rightarrow f$ in $L^2(\mathbb R)$ if $f_n(x) = f(x + x_n)$ where $x_n \rightarrow 0$

# 385 Reputation

 +10 How to prove that inverse Fourier transform of “1” is delta funstion? +10 $\|P\|_2 = 1$ implies $P^* = P$ +5 Shift Operator has no “square root”? +10 Inequality in Schwartz space

# 4 Questions

 12 Shift Operator has no “square root”? 1 If $a_n\to+\infty$, $b_n\to0$, how about $\prod_{k=1}^n(1+b_ne^{-a_k})$? 1 Bounded and invertible operator on dense subspace 0 Bounded operator on dense subspaces

# 23 Tags

 9 functional-analysis × 9 3 linear-algebra × 3 8 inequality × 3 3 multivariable-calculus 5 analysis × 5 3 calculus-of-variations 5 real-analysis × 2 2 limits × 3 4 pde × 2 2 integral-inequality × 2

# 1 Account

 Mathematics 385 rep 19