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      Questions tagged [inequalities]

      for questions involving inequalities.

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      5
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      1answer
      186 views

      Inequality involving tensor product of orthonormal unit vectors

      Let $e_1,...,e_r$ be the first $r$ standard basis of $\mathbb{R}^n, r<n$. Let $u_1,...,u_n$ be another orthonormal basis of $\mathbb{R}^n$. Let $\otimes$ be the tensor product on $\mathbb{R}^n$ and ...
      0
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      0answers
      132 views

      About a lemma of the Bowen Book [closed]

      I believe the passage I highlighted within the red square is wrong, therefore invalidating the proof of this motto. If it really is wrong. Does anyone know another demo and in which book can I find it?...
      0
      votes
      0answers
      60 views

      Bound of Coefficients of Fourier Series of Composition

      Let $f(x) = \sum_{n=0}^\infty f_ne^{inx} + \bar{f_n}e^{-inx}$ and $g(x) = \sum_{n=0}^\infty g_ne^{inx} + \bar{g_n}e^{-inx}$ where $f:\mathbb{R} \to \mathbb{R}$ and $g:\mathbb{R} \to \mathbb{R}$. Both ...
      2
      votes
      1answer
      153 views

      Is $ f(x(.)) := \int_{0}^{1} F ( x(t)) \; dt$ differentiable?

      Let $f : AC[0, 1] \to R$ be defined by $ f(x(.)) := \int_{0}^{1} F ( x(t)) \; dt$. Where, $AC[0, 1]$ is the set of absolutely continuous functions with the norm $W^{1,1}$, and $F: R^n \to R$ is ...
      0
      votes
      0answers
      59 views

      Is it possible to get a conjecture similar to Mandl's conjecture for a different arithmetic function of number theory, mainly related to primes?

      I'm curious to know if are in the literature analogous conjectures to the conjecture due to Mandl, I ask about these analogous conjectures for different sequences playing an important role in number ...
      1
      vote
      1answer
      119 views

      Bounding Coefficients of Dirichlet Series

      Consider the exponentiated Riemann-Zeta function $\zeta(s)^p$. If it is represented as $$\zeta(s)^p = \sum_{n=1}^\infty\frac{a_n}{n^s}$$ Is there any upper bound we can put on $|a_n|$ in terms of ...
      1
      vote
      1answer
      94 views

      A simple inequality that arises from the exact form for the prime-counting function and the second Hardy–Littlewood conjecture

      The germ of this post arises when I was trying to think what terms of the so-called exact form of the prime-counting function satisfy an inequality of the form $\text{term}(x+y)\leq \text{term}(x)+\...
      -1
      votes
      0answers
      85 views

      Finding the number of real roots of a power series

      Suppose we have a power series $f(x) = \sum_{i=0}^\infty a_nx^n$ that converges for all reals where $f(\pm1) \neq 0$. We want to find the number of real roots. In order to do that we find the roots ...
      20
      votes
      4answers
      2k views

      Prove that $\left(\frac{x^n+1}{x^{n-1}+1}\right)^n+\left(\frac{x+1}{2}\right)^n\geq x^n+1$

      Let $x>0$ and $n$ be a natural number. Prove that: $$\left(\frac{x^n+1}{x^{n-1}+1}\right)^n+\left(\frac{x+1}{2}\right)^n\geq x^n+1.$$ This question is very similar to many contests problems, but ...
      7
      votes
      2answers
      164 views

      $2$-norm distance between square roots of matrices

      Suppose two square real matrices $A$ and $B$ are close in the Schatten 1-norm, i.e. $\|A-B\|_1=\varepsilon$. Can this be used to put a bound on the Schatten 2-norm distance between their square roots. ...
      13
      votes
      4answers
      950 views

      $|L'(1,\chi)/L(1,\chi)|$

      Let $\chi$ be a primitive Dirichlet character $\mod q$, $q>1$. Is there a neat, simple way to give a good bound on $L'(1,\chi)/L(1,\chi)$? Assuming no zeroes $s=\sigma+it$ of $L(s,\chi)$ satisfy $\...
      3
      votes
      1answer
      133 views

      Can anyone give a reference to the proof of this concentration inequality?

      The following concentration inequality for the supremum of a Gaussian process indexed by a separable metric space appears here: http://math.iisc.ac.in/~manju/GP/6-Concentration%20and%20comparison%...
      1
      vote
      1answer
      52 views

      Matrix inequalities for the moment of the fixed Shatten norm

      Let $A_i, i=1, \ldots, N$ be real (or complex) matrices of the same dimension. Let $r_i, i=1, \ldots, N$ be independent Rademacher random variables. The following inequality gives a bound on the ...
      4
      votes
      1answer
      494 views

      Is there a error/typo in the proof related to Goormaghtigh equation in Yann Bugeaud's paper?

      I found the following theorem in a paper by Yann Bugeaud (page 12) , the theorem was not written in detail, to be specific,following two lines on page 13 were not understandable- I think this ...
      2
      votes
      1answer
      67 views

      Existence of stationary stochastic processes with very high correlation

      A question was recently asked by a new user, SomeoneHAHA, and then deleted by the user, after receiving an answer. I think the question and the answer (QA) to it may be of interest to some users. ...

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