Compact

Bump function

Bump function
  1. Is bump function smooth?
  2. What is a compact support?

Is bump function smooth?

While bump functions are smooth, they cannot be analytic unless they vanish identically. This is a simple consequence of the identity theorem. Bump functions are often used as mollifiers, as smooth cutoff functions, and to form smooth partitions of unity.

What is a compact support?

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For example, the function in its entire domain (i.e., ) does not have compact support, while any bump function does have compact support.

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