The purpose of this paper is to give some generalizations of de Branges Lemma for weighted spaces to obtain different approximation theorems in weighted spaces for algebras, vector subspaces or convex cones. We recall that the (original) de Branges Lemma (Proc Am Math Soc 10(5):822–824, 1959) was demonstrated for continuous scalar function on a compact space while, the weighted spaces are classes of continuous scalar functions on a locally compact space (e.g. the space of function with compact support, the space of bounded functions, the space of functions vanishing at infinity, the space of functions rapidly decreasing at infinity).

中文翻译：

---

加权空间中的De Branges引理和逼近

本文的目的是给出加权空间的de Branges引理的一般化，以获得代数，向量子空间或凸锥的加权空间中的不同近似定理。我们记得，（原始）de Branges引理（Proc Am Math Soc 10（5）：822–824，1959年）被证明用于紧空间上的连续标量函数，而加权空间是局部上连续标量函数的类。紧凑空间（例如具有紧凑支撑的功能空间，有界功能的空间，无穷大的功能空间，无穷大的功能空间）。