Tagged Questions

Norm is a function on a vector space $X$ which generalizes notion of length of vector in general vector spaces.

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Approximate decomposition of vector

Let $a,b,c$ be elements of a normed space such that $a+b=c$ and $\lVert a\rVert\leq\lVert c\rVert/2+\varepsilon$ and $\lVert b\rVert\leq\lVert c\rVert/2+\varepsilon$ for some small $\varepsilon>0$. ...
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Show a bound on the error

Suppose $g \in C[a,b]$, and $M(b-a) < 1$, and let $y$, $y_N$ $\in C[a,b]$ be the unique solutions of the equations, $y = g + Ky$ and $y_N = g + K_N y_N$. $y_N$ has been previously defined as an ...
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prove absolute integrability given square integrability

am trying to follow the outline of a proof in a book i am reading - must be missing something obvious, but would like to understand what exactly... $f$ is complex and square integrable over e. g. [0, ...
How do you know if $$||\frac{1}{\sqrt3},\frac{1}{\sqrt8}, ... , \frac{1}{\sqrt{n^2-1}}, ... ||_2$$ is finite. So this means is \bigg( \sum _{n=2}^{\infty} | \frac{1}{\sqrt{n^2-1}}|^2 \bigg) ^{\...
For a vector $v \in [0,1]^n$ and $p > 1$ we denote the p-norm of $v$ as: $||v||_p = (\sum_iv_i^p)^{\frac{1}{p}}$. where $v_i$ are the entries of $v$. Define the following (weird looking) function \$...