<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Questions tagged [real-analysis]

      Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

      Filter by
      Sorted by
      Tagged with
      0
      votes
      0answers
      18 views

      Weighted inner product of independent random unit vectors

      Let $u=(u_1,...,u_n)$ and $v=(v_1,...,v_n)$ be independent random unit vectors in $\mathbb{R}^n$. Let $\lambda=(\lambda_1,...,\lambda_n)$ be a fixed unit vector in $\mathbb{R}^n$. What is the ...
      0
      votes
      1answer
      72 views

      Lifting functions between $L^2$

      A map $\pi: X \to Y$, $\mu$ is the measure on $X$, and its push forward is defined by $\nu:=\pi_{*} \mu$. If given $f \in L^2(X, \mu)$, can we find $g \in L^2(Y, \nu)$ such that $g \circ \pi= f$, if $...
      1
      vote
      1answer
      32 views

      Reference request for (weak*) metrizability of a bounded space of signed Radon measures on a compact set

      I know the following is true and I know how to prove it (cf. exercise 50 on page 171 in Folland, Theorem 7.18 in Folland), but per my adviser's instructions, it would be better to find a source to ...
      1
      vote
      0answers
      225 views

      A (surprising?) expression for $e$

      I apologise if this is off topic. Consider the quantity $$ F(m,n,k)=\frac{(m)_k}{k!n^{k-1} } $$ where $m,n \in \mathbb{N}.$ For moderately large $n$, it seems that the approximation $$ \sum_{k=1}^{K} ...
      -4
      votes
      1answer
      145 views

      Formula for $1^x + 2^x + … + n^x$ when $x$ is complex [on hold]

      I would like to know if there is a formula for $$1^x + 2^x + ... + n^x$$ when $x$ is real or complex?
      2
      votes
      1answer
      115 views

      Weak convergence in $L^p$

      My question is probably very basic, sorry about that. Let $\{f_i\},\{g_i\}$ be two sequences converging to 0 weakly in $L^p[0,1]$ for any $p<\infty$. Can one conclude that $\int_0^1f_i(x)g_i(x) dx\...
      0
      votes
      0answers
      68 views

      Express $\zeta(n)$, in particular the Apéry's constant, in terms of series involving Gregory coefficients or the Schröder's integral

      The idea and motivation of this post is to know if it is possible to express integer arguments of the Riemann zeta function $\zeta(n)$, in particular $\zeta(3)$, in terms of series involving the so-...
      -1
      votes
      1answer
      126 views

      Denominator approximation sequence of a real number

      For any positive integer $[n]$, let $[n]=\{1,\ldots,n\}$. Let $r\in\mathbb{R}$. We define for every positive integer $n\in\mathbb{N}$ the minimal difference from a rational with denominator $\leq n$ ...
      4
      votes
      2answers
      180 views

      Comparing two limsup's

      Let $f\in L^2(0,\infty)$ be a positive, decreasing function. Is it then true that $$ \limsup_{x\to\infty} xf(x) = \limsup_{x\to\infty} \frac{1}{f(x)}\int_x^{\infty} f^2(t)\, dt $$ (and similarly for $\...
      1
      vote
      0answers
      30 views

      Generalization of Lagrange-Burmann to system of self-consistency equations

      In my research, I have come across a system of probability generating functions of the following form: $$H_1(x) = x A(H_1(x))B(H_2(x)) \text{,}$$ $$H_2(x) = x C(H_1(x))D(H_2(x)) \text{,}$$ and I am ...
      2
      votes
      1answer
      174 views

      Help in proving, that $\int_{0}^{\infty} \frac{1}{\Gamma(x)} d x=e+\int_{0}^{\infty} \frac{e^{-x}}{\pi^{2}+(\ln x)^{2}} d x$ using real methods only

      I hope this does not seem like a too easy question for Overflow. I would like to find an easier method than mine to prove the above statement for the Fransén-Robinson Constant. My first method was to ...
      2
      votes
      1answer
      176 views

      Limits of a family of integrals

      Assume $\lambda_1+\lambda_2=1$ and both $\lambda_1$ and $\lambda_2$ are positive reals. QUESTION. What is the value of this limit? It seems to exist. $$\lim_{n\rightarrow\infty}\int_0^1\frac{(\...
      8
      votes
      2answers
      235 views

      Low-degree polynomial approximation of the piecewise-linear function $x \mapsto \max(x, 0)$ on an interval $x \in [-R,R]$

      For $R > 0$, consider the piecewise-linear function $\sigma_R: [-R,R] \rightarrow \mathbb R^+$, defined by $\sigma_R(x) := \max(x,0)$. Question Given $\epsilon> 0$, find a "low-degree" ...
      2
      votes
      0answers
      45 views

      Extension of a $\delta$-subharmonic function that is subharmonic on a reduced domain

      Suppose $B$ is a ball in $\mathbb{R}^{m}$ and $u$ and $s$ are subharmonic on $B$. Suppose there is a closed subset $F$ of the closure of $B$ with no interior such that $v=u-s$ is subharmonic on $B\...
      1
      vote
      0answers
      44 views

      Removability of the isolated singularity of real analytic mappings with nondegenerate Jacobian

      Let $B^n=\{x\in \mathbf{R}^n: |x|<1\}$$(n>2)$. Consider real analytic mappings $f_1:B^n\setminus \{0\}\to B^n$, $f_2:B^n\setminus \{0\}\to \mathbf{R}^n$ and $f_3: B^n\setminus \{0\}\to S^n$ ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>

              江西麻将桌批发在哪里 切沃那不勒斯 微信竞彩足球 糖果炸弹官网 体彩排列5走势图 切沃对AC米兰预测 七乐彩走势图zhejiang 中秋嫦娥奔月 pp电子游戏 可爱水果老虎机