All Questions
3
questions
11
votes
1
answer
325
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Can a norm on polynomials be supermultiplicative?
A norm on a real algebra is supermultiplicative when $\lVert f\cdot g\rVert\geq\lVert f\rVert\cdot\lVert g\rVert$ for all $f$ and $g$ in the algebra.
Is there a supermultiplicative norm on $\mathbb R[...
- 5,726
5
votes
2
answers
256
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Can a norm on polynomials be "almost multiplicative", even for large degrees?
Definition: A norm on a real algebra is called almost multiplicative if there are positive constants $L$ and $U$ such that, for all $f$ and $g$ in the algebra,
$$L\lVert f\rVert\cdot\lVert g\rVert\;\...
- 5,726
2
votes
1
answer
98
views
Show that $\sum_{k=0}^{N} |P(k)| \leq C(N) \int_{0} ^{1} |P(t)| dt $. [closed]
I’m attending a functional analysis course and I am given to solve this problem as an exercise but I’m a little bit disoriented and I don’t know what tools I can use to get it.
Show that, for each $...
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