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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, 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, 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 wikiPageLength "13339".
- Non-analytic_smooth_function wikiPageOutDegree "67".
- Non-analytic_smooth_function wikiPageRevisionID "703380110".
- Non-analytic_smooth_function wikiPageWikiLink 0_(number).
- Non-analytic_smooth_function wikiPageWikiLink Analytic_continuation.
- Non-analytic_smooth_function wikiPageWikiLink Analytic_function.
- Non-analytic_smooth_function wikiPageWikiLink Analyticity_of_holomorphic_functions.
- Non-analytic_smooth_function wikiPageWikiLink Ball_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Borels_lemma.
- Non-analytic_smooth_function wikiPageWikiLink Bump_function.
- Non-analytic_smooth_function wikiPageWikiLink Category:Articles_containing_proofs.
- Non-analytic_smooth_function wikiPageWikiLink Category:Smooth_functions.
- Non-analytic_smooth_function wikiPageWikiLink Cauchy–Hadamard_theorem.
- Non-analytic_smooth_function wikiPageWikiLink Chain_rule.
- Non-analytic_smooth_function wikiPageWikiLink Complex_analysis.
- Non-analytic_smooth_function wikiPageWikiLink Complex_manifold.
- Non-analytic_smooth_function wikiPageWikiLink Complex_plane.
- Non-analytic_smooth_function wikiPageWikiLink Converse_(logic).
- Non-analytic_smooth_function wikiPageWikiLink Counterexample.
- Non-analytic_smooth_function wikiPageWikiLink Differentiable_function.
- Non-analytic_smooth_function wikiPageWikiLink Differentiable_manifold.
- Non-analytic_smooth_function wikiPageWikiLink Differential_geometry.
- Non-analytic_smooth_function wikiPageWikiLink Distribution_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Dyadic_rational.
- Non-analytic_smooth_function wikiPageWikiLink Essential_singularity.
- Non-analytic_smooth_function wikiPageWikiLink Euclidean_space.
- Non-analytic_smooth_function wikiPageWikiLink Exponential_function.
- Non-analytic_smooth_function wikiPageWikiLink Extreme_value_theorem.
- Non-analytic_smooth_function wikiPageWikiLink Fabius_function.
- Non-analytic_smooth_function wikiPageWikiLink File:Smooth_transition_from_0_to_1.png.
- Non-analytic_smooth_function wikiPageWikiLink Flat_function.
- Non-analytic_smooth_function wikiPageWikiLink Fourier_series.
- Non-analytic_smooth_function wikiPageWikiLink Function_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Functional_equation.
- Non-analytic_smooth_function wikiPageWikiLink Generalized_function.
- Non-analytic_smooth_function wikiPageWikiLink Injective_sheaf.
- Non-analytic_smooth_function wikiPageWikiLink Laurent_Schwartz.
- Non-analytic_smooth_function wikiPageWikiLink Mathematical_induction.
- Non-analytic_smooth_function wikiPageWikiLink Mathematics.
- Non-analytic_smooth_function wikiPageWikiLink Mollifier.
- Non-analytic_smooth_function wikiPageWikiLink Monomial.
- Non-analytic_smooth_function wikiPageWikiLink Natural_number.
- Non-analytic_smooth_function wikiPageWikiLink Norm_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Origin_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Partition_of_unity.
- Non-analytic_smooth_function wikiPageWikiLink Picard_theorem.
- Non-analytic_smooth_function wikiPageWikiLink Radius_of_convergence.
- Non-analytic_smooth_function wikiPageWikiLink Ratio_test.
- Non-analytic_smooth_function wikiPageWikiLink Real_line.
- Non-analytic_smooth_function wikiPageWikiLink Real_number.
- Non-analytic_smooth_function wikiPageWikiLink Reciprocal_rule.
- Non-analytic_smooth_function wikiPageWikiLink Sheaf_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Smoothness.
- Non-analytic_smooth_function wikiPageWikiLink Support_(mathematics).
- Non-analytic_smooth_function wikiPageWikiLink Taylor_series.
- Non-analytic_smooth_function wikiPageWikiLink Uniform_norm.
- Non-analytic_smooth_function wikiPageWikiLink Unit_interval.
- Non-analytic_smooth_function wikiPageWikiLink Weierstrass_M-test.
- Non-analytic_smooth_function wikiPageWikiLink Émile_Borel.
- Non-analytic_smooth_function wikiPageWikiLink File:Mollifier_Illustration.svg.
- Non-analytic_smooth_function wikiPageWikiLink File:Non-analytic_smooth_function.png.
- Non-analytic_smooth_function wikiPageWikiLink File:Smooth_non-analytic_function.png.
- Non-analytic_smooth_function wikiPageWikiLinkText "Non-analytic smooth function".
- Non-analytic_smooth_function wikiPageWikiLinkText "infinitely differentiable, non analytic".
- Non-analytic_smooth_function wikiPageWikiLinkText "non-analytic smooth function".
- Non-analytic_smooth_function wikiPageWikiLinkText "non-analytic smooth functions".
- Non-analytic_smooth_function wikiPageWikiLinkText "smooth but not analytic at any point".
- Non-analytic_smooth_function id "3081".
- Non-analytic_smooth_function title "Infinitely-differentiable function that is not analytic".
- Non-analytic_smooth_function wikiPageUsesTemplate Template:Main.
- Non-analytic_smooth_function wikiPageUsesTemplate Template:Planetmath_reference.
- Non-analytic_smooth_function wikiPageUsesTemplate Template:Reflist.
- Non-analytic_smooth_function subject Category:Articles_containing_proofs.
- Non-analytic_smooth_function subject Category:Smooth_functions.
- Non-analytic_smooth_function type Type.
- Non-analytic_smooth_function type Function.
- Non-analytic_smooth_function type Proof.
- Non-analytic_smooth_function type Type.
- 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, 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, like e.g.".
- Non-analytic_smooth_function label "Non-analytic smooth function".
- Non-analytic_smooth_function sameAs Q7048840.
- Non-analytic_smooth_function sameAs x).
- Non-analytic_smooth_function sameAs m.026hvc.
- Non-analytic_smooth_function sameAs Q7048840.
- Non-analytic_smooth_function wasDerivedFrom Non-analytic_smooth_function?oldid=703380110.
- Non-analytic_smooth_function depiction Non-analytic_smooth_function.png.
- Non-analytic_smooth_function isPrimaryTopicOf Non-analytic_smooth_function.