In operator theory, a multiplication operator is a linear operator Tf defined on some vector space of functions and whose value at a function φ is given by multiplication by a fixed function f. That is, T f φ ( x ) = f ( x ) φ ( x ) {\displaystyle T_{f}\varphi (x)=f(x)\varphi (x)\quad } for all φ in the domain of Tf, and all x in the domain of φ (which is the same as the domain of f).
In operator theory, a multiplication operator is a linear operator Tf defined on some vector space of functions and whose value at a function φ is given by multiplication by a fixed function f. That is, T f φ ( x ) = f ( x ) φ ( x ) {\displaystyle T_{f}\varphi (x)=f(x)\varphi (x)\quad } for all φ in the domain of Tf, and all x in the domain of φ (which is the same as the domain of f).
Source: Wikipedia "Multiplication operator" · CC BY-SA 4.0
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