Newbetuts
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New posts in real-analysis
Suppose $1\le p < r < q < \infty$. Prove that $L^p\cap L^q \subset L^r$.
real-analysis
analysis
measure-theory
lebesgue-integral
lp-spaces
Let $f$ be a cont. on $\mathbb{R}$ and define $G(x)=\int_0^{\sin (x)}f(t) dt $. Show that $G$ is differentiable on $\Bbb{R}$ and compute $G'$.
real-analysis
solution-verification
Is this sequence bounded ? (An open problem between my schoolmates !)
real-analysis
integration
limits
distribution-theory
Show $\sigma_{X}^{2}(t)=\begin{cases} x_{0}\frac{\beta}{\alpha}e^{\alpha t}[e^{\alpha t}-1], & \alpha \neq 0\\ x_{0}\beta t, & \alpha = 0 \end{cases}$
real-analysis
probability
integration
improper-integrals
stochastic-calculus
To find continuous functions on $\mathbb R$ which preserve certain algebraic structures
real-analysis
linear-algebra
abstract-algebra
continuity
$U\subset [0,\infty)$ is open and unbounded $\Rightarrow \exists x$ such that $U\cap \{nx;n\in \mathbb N\}$ is infinite.
real-analysis
general-topology
metric-spaces
How to show that the series of $\frac{\sin(n)}{\log(n)}$ converges?
calculus
real-analysis
sequences-and-series
convergence-divergence
A smooth nowhere analytic function such that all derivatives are monotone
real-analysis
continuity
examples-counterexamples
analyticity
monotone-functions
Proving algebraically $a^2+b^2\ge a^{\alpha}b^{2-\alpha}$ for $0\le\alpha\le2$ and $a,b\ge0$
real-analysis
linear-algebra
inequality
alternative-proof
Function satisfying $\lim_{x\to 0}\frac{f(ax)}{f(x)}=a$
calculus
real-analysis
Is it possible that $\sum a_{\sigma(n)}$ converges iff $\sum b_{\sigma(n)}$ diverges for every permutation $\sigma :\mathbb N\to \mathbb N$?
real-analysis
sequences-and-series
conditional-convergence
Comparison of $L^2$ and $L^1$ norms for functions
real-analysis
functional-analysis
analysis
understand what ∪n∈NUn = (0, 2) ⊃ (0, 1] means [closed]
real-analysis
probability-theory
analysis
discrete-mathematics
Second derivative: how should one think about?
real-analysis
calculus
Why do we need min to choose $\delta$?
calculus
real-analysis
analysis
limits
epsilon-delta
convergence of $\sum_{n=1}^\infty \frac{n^{-x} + 1}{|log(x)|^n +1}$ if $x>0$
real-analysis
calculus
sequences-and-series
Find $\int_0^1 \frac{x-1}{\ln (x)} \, dx$
real-analysis
integration
Are there functions $f(t)$ with $||f'(t)||_\infty < \infty$ such as their Fourier transform $F(w)$ makes $\int_{-\infty}^\infty|wF(w)|dw \to \infty$??
real-analysis
complex-analysis
derivatives
fourier-analysis
fourier-transform
Towards a Little proof of Fermat's last theorem
real-analysis
number-theory
diophantine-equations
generating-functions
Convex functions in integral inequality
real-analysis
probability
inequality
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