Lesson plan
Bump function
In mathematical analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used as cutoff functions, for example functions that are equal to 1 on a prescribed set and vanish outside a larger set, and as standard examples of kernels used to construct mollifiers. Some authors use the term more broadly for any compactly supported smooth function. Such functions are important examples of test functions, especially in distribution theory, but the terms "bump function" and "test function" are not synonymous in all contexts.
Article summary
In mathematical analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used as cutoff functions, for example functions that are equal to 1 on a prescribed set and vanish outside a larger set, and as standard examples of kernels used to construct mollifiers. Some authors use the term more broadly for any compactly supported smooth function. Such functions are important examples of test functions, especially in distribution theory, but the terms "bump function" and "test function" are not synonymous in all contexts.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.