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nonanalytic
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Not analytic |
Nonanalytic might refer to |
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In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not true, as demonstrated with the counterexample below. * One of the most important applications of smooth functions with compact support is the construction of so-called mollifiers, which are important in theories of generalized functions, e.g., Laurent Schwartz's theory of distributions. * The existence of smooth but non-analytic functions represents one of the main differences between differential geometry and analytic geometry. In terms of sheaf theory, this difference can be stated as follows: the sheaf of differentiable functions on a differentiable manifold is fine, in contrast with the analytic case. * The functions below are generally used to build up partitions of unity on differentiable manifolds. |