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# Questions tagged [inequalities]

for questions involving inequalities.

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### 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 ...
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?...
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 ...
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 ...
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 ...
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 ...
94 views

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%...
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 ...
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 ...
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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