A growth rate is said to be infra-exponential or subexponential if it is dominated by all

exponential growth Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a q ...

rates, however great the

doubling time The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things th ...

. A continuous function with infra-exponential growth rate will have a

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

that is a Fourier

hyperfunction In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato ...

. Examples of sub-exponential growth rates arise in the

analysis of algorithms In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...

, where they give rise to sub-exponential time complexity, and in the growth rate of groups, where a subexponential growth rate implies that a group is amenable.

References

Fourier hyperfunction
in the Encyclopedia of Mathematics Exponentials {{mathanalysis-stub