Nachbin's theorem (original) (raw)
In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below.
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below. (en) Em matemática, na área de análise complexa, o teorema de Nachbin (referente a Leopoldo Nachbin) é usado para estabelecer um limite no crescimento de uma função analítica. Este artigo fornecerá uma breve revisão das taxas de crescimento, incluindo a ideia de uma função de tipo exponencial. A classificação das taxas de crescimento baseadas na ajuda do tipo fornece uma ferramenta mais fina do que a notação grande de O ou de Landau, desde que um número de teoremas sobre a estrutura analítica da função delimitada e suas transformações integrais pode ser indicada. Em particular, o teorema de Nachbin pode ser usado para dar o domínio da convergência da transformada Borel generalizada, dada abaixo (pt) |
| dbo:wikiPageID | 4081361 (xsd:integer) |
| dbo:wikiPageLength | 6544 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1069893251 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Carlson's_theorem dbr:Mellin_transform dbr:Borel_summation dbr:Uniform_space dbr:Van_Wijngaarden_transformation dbr:Integral_transform dbr:Complete_space dbr:Complex_analysis dbr:Complex_plane dbr:Analytic_function dbr:Mathematics dbr:Norm_(mathematics) dbr:Entire_function dbr:Fréchet_space dbr:Leopoldo_Nachbin dbr:Cauchy's_integral_formula dbr:Cesàro_summation dbr:Divergent_series dbr:Lambert_summation dbr:Abelian_and_tauberian_theorems dbc:Integral_transforms dbc:Summability_methods dbc:Theorems_in_complex_analysis dbr:Landau_notation dbr:Laplace_transform dbr:Big_O_notation dbr:Mittag-Leffler_summation dbr:Phragmén–Lindelöf_principle dbr:Ratio_test dbr:Infimum dbr:Euler_summation dbr:Integral_transforms dbr:Topological_space dbr:Contour_of_integration dbr:Complex_variable |
| dbp:author | A.F. Leont'ev (en) |
| dbp:id | B/b017190 (en) F/f041990 (en) |
| dbp:title | Borel transform (en) Function of exponential type (en) |
| dbp:wikiPageUsesTemplate | dbt:Springer dbt:About dbt:Main dbt:Short_description |
| dct:subject | dbc:Integral_transforms dbc:Summability_methods dbc:Theorems_in_complex_analysis |
| rdf:type | yago:WikicatTheoremsInComplexAnalysis yago:WikicatSummabilityMethods yago:Ability105616246 yago:Abstraction100002137 yago:Cognition100023271 yago:Communication100033020 yago:Know-how105616786 yago:Message106598915 yago:Method105660268 yago:Proposition106750804 yago:PsychologicalFeature100023100 yago:Statement106722453 yago:Theorem106752293 |
| rdfs:comment | In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below. (en) Em matemática, na área de análise complexa, o teorema de Nachbin (referente a Leopoldo Nachbin) é usado para estabelecer um limite no crescimento de uma função analítica. Este artigo fornecerá uma breve revisão das taxas de crescimento, incluindo a ideia de uma função de tipo exponencial. A classificação das taxas de crescimento baseadas na ajuda do tipo fornece uma ferramenta mais fina do que a notação grande de O ou de Landau, desde que um número de teoremas sobre a estrutura analítica da função delimitada e suas transformações integrais pode ser indicada. Em particular, o teorema de Nachbin pode ser usado para dar o domínio da convergência da transformada Borel generalizada, dada abaixo (pt) |
| rdfs:label | Nachbin's theorem (en) Teorema de Nachbin (pt) |
| owl:sameAs | freebase:Nachbin's theorem yago-res:Nachbin's theorem wikidata:Nachbin's theorem dbpedia-pt:Nachbin's theorem https://global.dbpedia.org/id/4rnVv |
| prov:wasDerivedFrom | wikipedia-en:Nachbin's_theorem?oldid=1069893251&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Nachbin's_theorem |
| is dbo:wikiPageRedirects of | dbr:Psi-type dbr:Function_of_exponential_type dbr:Generalized_Borel_transform dbr:Nachbin_resummation dbr:Nachbin_theorem |
| is dbo:wikiPageWikiLink of | dbr:Mellin_inversion_theorem dbr:Residue_theorem dbr:Integral_transform dbr:Leopoldo_Nachbin dbr:Cauchy's_integral_formula dbr:Line_integral dbr:List_of_Brazilian_mathematicians dbr:List_of_exponential_topics dbr:Borel_transform dbr:Laplace_transform dbr:Big_O_notation dbr:Mittag-Leffler_summation dbr:Recife dbr:Exponential_type dbr:List_of_theorems dbr:Psi-type dbr:Function_of_exponential_type dbr:Generalized_Borel_transform dbr:Nachbin_resummation dbr:Nachbin_theorem |
| is foaf:primaryTopic of | wikipedia-en:Nachbin's_theorem |