Pekfunktion

Pekfunktion is a term that does not have a single, universally accepted definition and its meaning can vary by language and field. In practice, it is sometimes encountered as a calque or shorthand for related concepts such as peak or peaking functions, and its precise interpretation depends on context. Some Scandinavian sources may use pekfunktion to refer loosely to a function that exhibits a peak behavior at a specific point or location.

In mathematics, a closely related and widely used concept is the peak function (also called a peaking function). In complex analysis, a peak function for a domain D is a function that is holomorphic on D and continuous on the closure of D, attaining its maximum modulus at a prescribed boundary point p while remaining strictly smaller than that maximum at all other boundary points. More generally, peak functions are used to study boundary behavior of holomorphic functions and to separate points on the boundary.

In real analysis and approximation theory, analogous ideas appear as bump functions or smooth peak functions: functions with compact support that achieve their maximum at a chosen point, often rescaled so that the maximum value is 1. Such functions are useful in constructions for partitions of unity, approximation processes, and localization arguments.

Etymology and usage notes: pekfunktion is not a standard mathematical term in major reference works, and its meaning is highly dependent on the source language and discipline. When encountering pekfunktion in texts, it is advisable to consult nearby definitions or the author’s clarification to determine whether the reference is to a peak/peaking function, a pointer-related concept in programming, or another domain-specific usage.

See also: peak function, peaking set, bump function, partition of unity.