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Results tagged with interpolation-spaces
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user 37266
5
votes
1
answer
252
views
Relation between two different functionals: $\lVert p^{-\max}_{-\varepsilon}\rVert$ and $\ka...
Given a non-negative sequence $p=(p_i)_{i\in\mathbb{N}}\in \ell_1$ such that $\lVert p\rVert_1 = 1$,we define the two following quantities, for every $\varepsilon \in (0,1]$.
Assuming, without loss …
- 1,372
2
votes
0
answers
183
views
Properties of the optimal decomposition for the $K$-functional between $\ell_1$ and $\ell_2$
Background: For any fixed $t> 0$, the $K$-functional defines a norm on the space $\ell_1+\ell_2$:
$$
\lVert a\rVert_{K(t)} = \inf\{\lVert a'\rVert_1+ t\lVert a''\rVert_2 : a'\in\ell_1,\ a''\in\ell_2,\ …
- 1,372