PROPERTIES OF A RUDIN'S ORTHOGONAL FUNCTION WHICH IS A LINEAR COMBINATION OF TWO INNER FUNCTIONS

摘要

φ is called a Rudin's (orthogonal) function if φ is a function in H~∞ and the different nonnegative powers of φ are orthogonal in H~2. When φ is a multiple of an inner function and φ(0) = 0, φ is a Rudin's function. Sundberg and Bishop showed that a Rudin's function is not necessarily a multiple of an inner function. We study a Rudin's function which is a linear combination of two inner functions or a polynomial of an inner function.