Euduardo

### Questions (10)

 2 Minimizing the value of integral under certain conditions 2 Exercise 4.33 in Brezis functional analysis. 2 Showing that $\sin x\;f(\sin x)\;f^\prime(\cos x)+\cos x\;f(\cos x)\;f^\prime(\sin x)=\frac{2}{\pi\sin x\cos x}$ for $f(x)$ defined by a series 1 Probability problem (Durrett 4.7.4.) Exchangeable Sequence of Random Variables. 1 Use of Holder inequality in gradient estimate for harmonic function.

### Reputation (190)

 +10 Minimizing the value of integral under certain conditions +10 Let $I=[0, \infty)$ and $f:I \to R$ a mensurable function such that $|f(t)| \leq \frac{t^\alpha}{1+t}$, where $0 <\alpha <1$. +5 Probability problem (Durrett 4.7.4.) Exchangeable Sequence of Random Variables. +10 If $a_1=\tan\alpha$ and $a_{n+1}=a_n^2\cos^2\alpha+\sin^2\alpha$, show $(a_n)$ is monotone and bounded; compute related limits

 3 $f$ holomorphic in $\mathbb{D}$. Prove $f$ has a zero in $\mathbb{D}$ 2 If $a_1=\tan\alpha$ and $a_{n+1}=a_n^2\cos^2\alpha+\sin^2\alpha$, show $(a_n)$ is monotone and bounded; compute related limits 2 Let $I=[0, \infty)$ and $f:I \to R$ a mensurable function such that $|f(t)| \leq \frac{t^\alpha}{1+t}$, where $0 <\alpha <1$. 0 Compute integral in unbounded area

### Tags (32)

 4 real-analysis × 2 0 functional-analysis × 3 3 complex-analysis 0 random-variables × 3 2 calculus × 2 0 martingales × 2 2 sequences-and-series × 2 0 hilbert-spaces × 2 2 lebesgue-integral 0 self-adjoint-operators × 2

### Account (1)

 Mathematics 190 rep 8