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- Non-analytic_smooth_function abstract "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, with this article constructing a counterexample.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, like 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.".
- Non-analytic_smooth_function thumbnail Non-analytic_smooth_function.png?width=300.
- Non-analytic_smooth_function wikiPageID "421463".
- Non-analytic_smooth_function wikiPageRevisionID "605211336".
- Non-analytic_smooth_function hasPhotoCollection Non-analytic_smooth_function.
- Non-analytic_smooth_function id "3081".
- Non-analytic_smooth_function title "Infinitely-differentiable function that is not analytic".
- Non-analytic_smooth_function subject Category:Articles_containing_proofs.
- Non-analytic_smooth_function subject Category:Smooth_functions.
- Non-analytic_smooth_function type Abstraction100002137.
- Non-analytic_smooth_function type Function113783816.
- Non-analytic_smooth_function type MathematicalRelation113783581.
- Non-analytic_smooth_function type Relation100031921.
- Non-analytic_smooth_function type SmoothFunctions.
- Non-analytic_smooth_function comment "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, with this article constructing a counterexample.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, like e.g.".
- Non-analytic_smooth_function label "Exp(-1/x)".
- Non-analytic_smooth_function label "Non-analytic smooth function".
- Non-analytic_smooth_function sameAs x).
- Non-analytic_smooth_function sameAs m.026hvc.
- Non-analytic_smooth_function sameAs Q7048840.
- Non-analytic_smooth_function sameAs Q7048840.
- Non-analytic_smooth_function sameAs Non-analytic_smooth_function.
- Non-analytic_smooth_function wasDerivedFrom Non-analytic_smooth_function?oldid=605211336.
- Non-analytic_smooth_function depiction Non-analytic_smooth_function.png.
- Non-analytic_smooth_function isPrimaryTopicOf Non-analytic_smooth_function.
