About: Pseudo-differential operator

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In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric in a non-Archimedean space.

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rdf:type	Thing software yago:WikicatPartialDifferentialEquations yago:Abstraction100002137 yago:Communication100033020 yago:DifferentialEquation106670521 yago:Equation106669864 yago:Function113783816 yago:MathematicalRelation113783581 yago:MathematicalStatement106732169 yago:Message106598915 yago:Operator113786413 yago:PartialDifferentialEquation106670866 yago:Relation100031921 yago:WikicatGeneralizedFunctions yago:Statement106722453 yago:WikicatDifferentialEquations yago:WikicatDifferentialOperators
rdfs:label	Pseudodifferentialoperator (de) Opérateur pseudo-différentiel (fr) 유사 미분 연산자 (ko) 擬微分作用素 (ja) Pseudo-differential operator (en) Operador pseudodiferencial (pt) 伪微分算子 (zh) Псевдодиференціальний оператор (uk)
rdfs:comment	Ein Pseudodifferentialoperator ist eine Erweiterung des Konzepts des Differentialoperators. Sie sind ein wichtiger Bestandteil der Theorie der partiellen Differentialgleichungen. Die Grundlagen der Theorie stammen von Lars Hörmander. Eingeführt wurden sie 1965 durch Joseph Kohn und Louis Nirenberg. Ihr Studium bildet einen wichtigen Teil der mikrolokalen Analysis. (de) En analyse mathématique, un opérateur pseudo-différentiel est une extension du concept familier d'opérateur différentiel, permettant notamment l'inclusion d'ordres de dérivation non entiers. Ces opérateurs pseudo-différentiels sont abondamment utilisés dans la théorie des équations aux dérivées partielles et en théorie quantique des champs. (fr) In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric in a non-Archimedean space. (en) 解析学における擬微分作用素（ぎびぶんさようそ、英: pseudo-differential operator）は、微分作用素を一般化するものである。1965 年以降、ラース・ヘルマンダー等により急速に研究されて来た。偏微分方程式論の代表的なテーマの一つであるが、マルコフ過程・・ポテンシャル理論との関わりも深い。物理学では量子力学や量子統計力学と関係がある。 (ja) 조화해석학에서 유사 미분 연산자(類似微分演算子, 영어: pseudodifferential operator, 약자 ΨDO)는 미분 연산자와, 매끄러운 함수와의 곱셈의 공통된 일반화이다. 푸리에 변환 공간에서 위치와 운동량에 의존하는 임의의 매끄러운 함수를 곱한 뒤 다시 역변환시키는 연산이다. (ko) Um operador pseudo-diferencial é uma generalização do conceito de operador diferencial. É uma parte fundamental da teoria das equações diferenciais parciais. Os fundamentos da teoria foram desenvolvidos por Lars Hörmander. (pt) 数学分析中，伪微分算子是微分算子的推广。伪微分算子在偏微分方程和量子场论等领域有广泛的应用。 (zh) У математичному аналізі псевдодиференціальний оператор є розширенням поняття диференціальний оператор, що діє у функціональних просторах на на евклідових просторах чи, більш загально, диференційованих многовидах і записується за допомогою деякої функції, що зазвичай називається символом псевдодиференціального оператора. Дана функція задовольняє оцінки похідних певного типу, аналогічні оцінкам похідних многочленів, що є символами диференціальних операторів. (uk)
dcterms:subject	Generalized functions Harmonic analysis Microlocal analysis Differential operators Partial differential equations Functional analysis
Wikipage page ID	973479 (xsd:integer)
Wikipage revision ID	1124808623 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum field theory Generalized functions Joseph J. Kohn Integral transform Compact support Harmonic analysis Mathematical analysis Non-Archimedean Oscillatory integral operator Louis Nirenberg Singular integral Microlocal analysis Microlocal analysis Fourier transform Partial differential equations Differential operator Fourier integral operator Atiyah–Singer index theorem Differential operators Partial differential equations Functional analysis Lars Hörmander Differential algebra Distribution (mathematics) Mark S. Joshi Polynomial Schwartz distribution Michael E. Taylor Operational calculus Hörmander Fourier's inversion formula Fourier multiplier Francois Treves Elliptic differential operator Multi-index dbr:Pseudo-differential_equations dbr:Sato's_fundamental_theorem
Link from a Wikipage to an external page	https://arxiv.org/abs/math.AP/9906155
sameAs	Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator Pseudo-differential operator
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Authority_control dbt:Citation dbt:Cite_book dbt:ISBN dbt:NumBlk dbt:Reflist dbt:Short_description

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