Riesz基的规范正交化及其性质

Normal Orthogonalization of Riesz Basis and Its Properties

类比Euclid空间中一组线性无关的向量经过Schmidt正交化法得到规范正交基的方法,将Hilbert空间中一组下界为A上界为B的Riesz基正交化为与之对应的规范正交基,并给出一个典型实例来验证方法的有效性。另外给出同一Hilbert空间H中两组Riesz基之间的联系。

By analogy with the process of a group of linearly independent vectors in Euclid space,the normal orthogonal basis through Schmidt orthogonalization was acquired.A group of Riesz basis with upper bound A and lower bound B in Hilbert space was orthogonalized into corresponding normal orthogonal basis.A typical example was given to verify the effectiveness of the method.In addition,the relation between the two sets of Riesz basis in the same Hilbert space H was demonstrated.