Conditions under which the system of dilations and translations of a function f in a symmetric space X is a representing system in X are found. Previously a similar result was known only for the spaces L_p, 1 ⩽ p < ∞. In particular, each function f with \(\int_0^1 {f(t)dt \ne 0} \) in a Lorentz space Λ_ϕ generates an absolutely representing system of dilations and translations in this space if and only if the function ϕ(t) is submultiplicative. The key role in the proof is played by the notion of the multiplier space with respect to tensor product.

中文翻译：

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用膨胀和平移表示对称空间中的函数

根据该胀缩和的函数的翻译的系统条件˚F在对称空间X是在代表系统X被发现。先前类似的结果被称为仅在空间大号_p，1个⩽ p <∞。特别地，每个功能˚F与\（\ INT_0 ^ 1 {F（T）dt的\ NE 0} \）中的洛伦兹空间Λ _φ在该空间中产生扩张术和翻译的绝对表示系统当且仅当函数φ（t）是可乘的。证明中的关键作用是关于张量积的乘数空间的概念。