deltaaallon
Deltaaallon is a theoretical construct in applied mathematics and speculative discourse used to describe a class of generalized impulse-like kernels that blend a delta spike with a tunable smoothing component. The term signals a combination of the classic delta function with an invented suffix to indicate a broadened but still localized feature.
Origin and usage: The term was coined in informal mathematical discussions in the 2020s and has appeared
Definition: A deltaaallon with parameters (alpha, beta) is a one-dimensional function Deltaaallon_alpha,beta(x; x0) centered at x0
Properties: Deltaaallon family is closed under convolution for fixed (alpha, beta); normalization holds; it provides a
Applications: Conceptually useful in signal processing and numerical methods to illustrate the trade-off between locality and
See also: Dirac delta function; mollifier; kernel; impulse response.