Bernstein's Theorem
Bernstein's Theorem is a fundamental result in the field of complex analysis, specifically concerning the behavior of entire functions. It states that if an entire function has a bounded derivative, then the function itself must be a polynomial. This means that the growth of the function is limited, leading to a simpler form.
The theorem highlights the relationship between the growth of a function and its differentiability. It provides insight into the structure of entire functions, showing that those with certain growth restrictions cannot be too complex, reinforcing the idea that polynomials are the simplest types of entire functions.