TeXipedia

ast

Represents a binary operation denoted by an asterisk symbol, commonly used in mathematical expressions for multiplication or convolution.

Overview

Serves as a versatile mathematical operator that appears frequently in algebra, analysis, and advanced mathematics.

  • Often used to denote multiplication when a standard × or · might be ambiguous
  • Common in group theory to represent binary operations or product structures
  • Appears in functional analysis for convolution operations
  • Used in computer science notation for pointer dereferencing or wildcard operations
  • Particularly useful when multiple different multiplication-like operations need to be distinguished in the same context

Examples

Multiplication operator in mathematical expressions

x∗y=y∗xx \ast y = y \ast x 
x \ast y = y \ast x

Convolution operation between functions

(f∗g)(t)=∫−∞∞f(τ)g(t−τ) dτ(f \ast g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)\,d\tau 
(f \ast g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)\,d\tau

Group operation notation in abstract algebra

G={a,b,c} with operation ∗G = \{a, b, c\} \text{ with operation } \ast 
G = \{a, b, c\} \text{ with operation } \ast