Operaattoriteoria
Operaattoriteoria, often translated as operator theory, is a branch of mathematics that studies algebraic structures known as operators, which are typically functions that map a vector space to itself. These operators are often linear, meaning they preserve vector addition and scalar multiplication. The study of operators is fundamental to many areas of mathematics, including functional analysis, quantum mechanics, and differential equations.
The core of operator theory lies in understanding the properties of these operators. This includes investigating
Operator theory has profound applications. In quantum mechanics, observables like position and momentum are represented by