symmetric monoidal (∞,1)-category of spectra
A convolution product is the binary operation on ring-valued (or more generally magma-valued) functions on a group or more generally on the set of morphisms of a groupoid, which is given by summing or more generally integrating products of values on complementary elements of the schematic form
where denotes the inverse element or more generally the inverse morphism of .
For example if is a finite group, then this defines the group algebra, or more generally if is a suitable topological group or Lie group or more generally a suitably topological groupoid or Lie groupoid, then an integral-version of this formula defines the groupoid convolution algebra.
Often the convolution product is considered in analysis for suitably integrable functions on the real line regarded as a group with respect to addition of real numbers:
This generalizes to a convolution product of distributions.
These convolution products play a central role in Fourier analysis.
A categorification of the concept of convolution is the concept of Day convolution.
Last revised on November 27, 2023 at 22:22:14. See the history of this page for a list of all contributions to it.