When concepts (properties, operations, etc.) on a set are extended to functions by treating each function value in isolation, the extended concept is often qualified with the word pointwise. One example is pointwise convergence of functions—a sequence of functions converges pointwise to a function if for all .
An important of pointwise concepts are the pointwise operations—operations defined on functions by applying the operations to function values separately for each point in the domain of definition. These include
|(pointwise multiplication by scalar)|
An example of an operation on functions which is not pointwise is the convolution (http://planetmath.org/Convolution) product.
|Date of creation||2013-03-22 15:25:00|
|Last modified on||2013-03-22 15:25:00|
|Last modified by||lars_h (9802)|