Blaschke products

Blaschke products are special mathematical functions used in complex analysis, particularly within the unit disk (all points inside a circle with radius 1). They are constructed by multiplying simple factors that each "zero in" on a specific point inside the disk. These functions are bounded, meaning they stay within a certain size, and they map the unit disk onto itself. They’re important for understanding how complex functions behave, especially in relation to their zeros, and are used in areas like signal processing, control theory, and mathematical analysis to build or analyze functions with prescribed zeros inside the disk.