Namespaces
Variants
Actions

Pointwise operation

From Encyclopedia of Mathematics
Revision as of 19:59, 7 January 2015 by Richard Pinch (talk | contribs) (See also: Pointwise order)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

2020 Mathematics Subject Classification: Primary: 08-XX [MSN][ZBL]

Extension of an algebraic operation $\star$ on a set $X$ to a set of functions on a set $Y$ taking values in $X$. If $f, g$ are functions taking values in $X$ then the pointwise extension of a binary operation $\star$ is $$ f \star g : y \mapsto f(y) \star g(y)\,\ \ \text{for each}\ y \in Y \ . $$ The terms "pointwise addition", "pointwise multiplication" are also used. Algebraic operations of different signature have analogous pointwise extension.

This may be distinguished from such operations as convolution of functions, where the value of $f*g$ at $y$ does not depend solely on the values $f(y), g(y)$. See also Pointwise convergence.

See also Pointwise order.

How to Cite This Entry:
Pointwise operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointwise_operation&oldid=36145