Equação integral de Fredholm

Em matemática, a equação integral de Fredholm é uma equação integral cuja solução origina a teoria de Fredholm, o estudo dos núcleos de Fredholm e operadores de Fredholm. A equação integral foi estudada por Erik Ivar Fredholm.

Equação do primeiro tipo

Equações integrais, de modo geral, são comuns e aparecem de diferentes formas (Fourier, Laplace, Hankel, etc.). Elas diferem entre si em seus núcleos (definido a seguir). O que distingue as equações integrais de Fredholm é que elas são equações integrais nas quais os limites de integração são constantes. Isto é o contrário das equações integrais de Volterra.

Uma equação integral de Fredholm homogênea do primeiro tipo é escrita como

,

e o problema é, dado o núcleo contínuo K(t,s) e a função g(t), determinar a função f(s).

Se o núcleo é uma função somente da diferença de seus argumentos, ou seja, , e os limites de integração são , então o lado direito da equação pode ser reescrito como uma convolução das funções K e f, e portanto a solução é dada por

onde e são as transformadas de Fourier direta e inversa, respectivamente.

Equação do segundo tipo

Uma equação integral de Fredholm não-homogênea do segundo tipo é dada por

.

Dado o núcleo K(t,s) e a função , o problema é determinar a função . Um procedimento padrão para resolver este problema é usar o formalismo resolvente; expressa como uma série, a solução é conhecida como série de Liouville-Neumann.

Teoria geral

A teoria geral subjacente às equações de Fredholm é conhecida como teoria de Fredholm. Um dos principais resultados é que o núcleo K é um operador compacto, conhecido como operador de Fredholm. A condição de ser compacto pode ser mostrada invocando equicontinuidade. Como operador, ele tem uma teoria espectral que pode ser entendida em termos de um espectro discreto de autovalores que tendem a zero.

Applicações

As equações de Fredholm surgem naturalmente na teoria de processamento de sinais, mais notadamente no famoso problema de concentração espectral popularizado por David Slepian. Em mecânica computacional, formam a base do método dos elementos de contorno.

Ver também

Refereências

Read other articles:

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (مارس 2016) عبد الله عبدربه معلومات شخصية الميلاد 1379الرياض مركز اللعب مهاجم الجنسية السعودية المسيرة الاحترافية1 سنوا...

 

Untuk nama tempat di Iran, lihat Tanak, Iran. Bagian dari serial tentangAgama Yahudi Mazhab Ortodoks (HarediHasidikModern) Konservatif Reformasi (Klasik) Karaite Rekonstruksionis Pembaharuan Humanistik Haymanot Filsafat Prinsip kepercayaan Kabbalah Mesias Etik Bangsa pilihan Nama-nama Tuhan Gerakan Musar Pustaka Tanakh (TorahNevi'imKetuvim) Ḥumash Siddur Piyutim Zohar Rabbinik (TalmudMidrashTosefta) Syariat Taurat Mishneh Tur Shulchan Aruch Mishnah Berurah Aruch HaShulchan Kashrut Tzni...

 

スーパー戦隊シリーズ > 手裏剣戦隊ニンニンジャー このページのノートに、このページに関する注意があります。(2014年12月)注意の要約:「○年ぶり」などの記述について テレビ番組・中継内での各種情報(終了した番組・中継を含みます)は、DVDやBlu-rayなどでの販売や公式なネット配信、または信頼できる紙媒体またはウェブ媒体が紹介するまで、出典とし...

Internet TV service For other uses, see Joost (disambiguation). Screenshot The Joost homepage in May 2009Developer(s)Joost N.V.Final releasenone (n/a) [±] K.K.Preview release1.1.7 / 18 June 2008; 15 years ago (2008-06-18) Operating systemWindows XP, Vista;Mac OS X (x86 only), iOS, PlayStation 3Available inEnglishTypeP2PTVLicenseFreewareWebsitewww.joost.com Joost (/ˈdʒuːst/) was an Internet TV service, created by Niklas Zennström and Janus Friis (founders of ...

 

UFC Fight Night: Joanna vs. Waterson Detalhes Promoção Ultimate Fighting Championship Data 02019-10-12 12 de outubro de 2019 Local Amalie Arena Cidade Tampa, Flórida Público 10.597 Cronologia UFC 243: Whittaker vs. Adesanya UFC Fight Night: Joanna vs. Waterson UFC on ESPN: Reyes vs. Weidman UFC Fight Night: Joanna vs. Waterson (também conhecido como UFC Fight Night 161 ou UFC on ESPN+ 19) foi um evento de MMA produzido pelo Ultimate Fighting Championship no dia 12 de outubro de 2019, na ...

 

  Faisán verde Macho en Japón Hembra en JapónEstado de conservaciónPreocupación menor (UICN 3.1)[1]​TaxonomíaReino: AnimaliaFilo: ChordataClase: AvesOrden: GalliformesFamilia: PhasianidaeGénero: PhasianusEspecie: P. versicolor(Vieillot, 1825)Sinonimia Phasianus colchicus versicolor [editar datos en Wikidata] El faisán verde (Phasianus versicolor)[2]​ es una especie de ave galliforme de la familia Phasianidae endémica del Japón.[3]​ Es el ave nac...

Ботанічний заказник загальнодержавного значення «Джарилгацький» 46°01′21″ пн. ш. 32°59′32″ сх. д. / 46.02268400002777327° пн. ш. 32.99231200002777342° сх. д. / 46.02268400002777327; 32.99231200002777342Координати: 46°01′21″ пн. ш. 32°59′32″ сх. д. / 46.02268400002777327° пн. ...

 

الورم العصبي الليفي من النوع الأول Café au lait spot characteristic of NF1.Café au lait spot characteristic of NF1. معلومات عامة الاختصاص علم الوراثة الطبية،  وطب الجهاز العصبي[1]  من أنواع ورام ليفي عصبي،  ومرض  الوبائيات انتشار المرض 0.00026998 [2]0.000128 [2]0.000217 (1 يناير 1978)[2]0.000241 [2]0.0004...

 

Stanka Slatewa Medaillenspiegel Ringerin Bulgarien Olympische Spiele Silber 2008 Peking bis 72 kg Silber 2012 London bis 72 kg Weltmeisterschaft Gold 2006 Guangzhou bis 72 kg Gold 2007 Baku bis 72 kg Gold 2008 Tokio bis 72 kg Bronze 2009 Herning bis 72 kg Gold 2010 Moskau bis 72 kg Gold 2011 Istanbul bis 72 kg Europameisterschaft Bronze 2005 Warna bis 72 kg Gold 2006 Moskau bis 72 kg Gold 2007 Sofia bis 72 kg Gold 2008 Tampere bis 72 ...

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Relapse EP – news · newspapers · books · scholar · JSTOR (October 2023) (Learn how and when to remove this template message) 2002 EP by OceansizeRelapseEP by OceansizeReleased21 October 2002RecordedThe Work StudioGenreNew progLength22:17LabelBeggar...

 

Een soldaat die een roer met beide handen horizontaal houdt, richt en vuurt. Omstreeks 1600 uit de instructies voor het hanteren van de roer (collectie: Rijksmuseum Amsterdam) Het roer of vuurroer was een gladloops vuurwapen uit de zestiende en zeventiende eeuw. Het was een verkleinde uitvoering van het musket. Etymologie Het woord roer is afkomstig van het Duitse Rohr, wat buis betekent. Opvallend genoeg werd een ander Duits woord voor buis, Büchse, eveneens vernederlandst naar bus en buks....

 

Virus Epstein-Barr Sel leukemia berisi virus Epstein Barr (berwarna hijau). Klasifikasi virus Grup: Grup I (dsDNA) Famili: Herpesviridae Genus: Lymphocryptovirus Spesies: Human herpesvirus 4 (HHV-4) Virus Epstein-Barr, juga disebut Virus herpes manusia 4 adalah virus dari famili herpes (yang juga terdapat virus herpes simplex dan Sitomegalovirus), dan merupakan salah satu virus yang paling umum pada manusia. Banyak orang terinfeksi dengan Virus Epstein-Barr yang sering asimtomatik tetapi umum...

Sint-Corneliuskerk De Sint-Corneliuskerk is de parochiekerk van de tot de Vlaams-Brabantse plaats Grimbergen behorende wijk Molenveld, die zich bevindt in de Tangedallaan 34. Geschiedenis In 1960 werd deze tegen de kom van Vilvoorde gelegen wijk een zelfstandige parochie. In 1961 werd een noodkerk aangekocht. Dit gebouw was voorheen het restaurant Moeder Avia bij de luchthaven Melsbroek en werd tot noodkerk omgebouwd. Een definitieve kerk werd nooit gebouwd. Gebouw Het betreft een eenvoudige ...

 

1967 British film by Freddie Francis This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Torture Garden film – news · newspapers · books · scholar · JSTOR (January 2020) (Learn how and when to remove this template message) Torture GardenTheatrical release posterDirected byFreddie FrancisWritten byRobert Blo...

 

Light from the stars For other uses, see Starlight (disambiguation). Starry sky crossed with the Milky Way and a meteor Starlight is the light emitted by stars.[1] It typically refers to visible electromagnetic radiation from stars other than the Sun, observable from Earth at night, although a component of starlight is observable from Earth during daytime. Sunlight is the term used for the Sun's starlight observed during daytime. During nighttime, albedo describes solar reflections fr...

Historic house in Florida, United States This article lacks inline citations besides NRIS, a database which provides minimal and sometimes ambiguous information. Please help ensure the accuracy of the information in this article by providing inline citations to additional reliable sources. (November 2013) (Learn how and when to remove this template message) United States historic placeWhite HouseU.S. National Register of Historic Places Show map of FloridaShow map of the United StatesLocation...

 

Grade II listed lighthouse in the United kingdom LighthouseOrfordness Lighthouse Orfordness LighthouseLocationOrfordness SuffolkEnglandOS gridTM4498348865Coordinates52°05′02″N 1°34′27″E / 52.083940°N 1.574246°E / 52.083940; 1.574246TowerConstructed1637 (first)Constructionbrick towerAutomated1965Height30 m (98 ft)Shapetapered cylindrical tower with balcony and lanternMarkingswhite tower with two red bands, white lanternOperatorOrfordness Lighth...

 

American travel writer and novelist (born 1941) Paul TherouxBornPaul Edward Theroux (1941-04-10) April 10, 1941 (age 82)Medford, Massachusetts, U.S.Occupation Novelist travel writer short story writer literary critic EducationUniversity of MaineUniversity of Massachusetts, Amherst (BA)Period1967–presentSpouse Anne Castle ​ ​(m. 1967; div. 1993)​ Sheila Donnelly ​(m. 1995)​ChildrenMarcel TherouxLouis TherouxRel...

Ancient Chinese minister and monarch (1000s BCE) For the film, see Jiang Ziya (film) Duke Tai of Qi redirects here. For the later Qi ruler with the same title, see Duke Tai of Tian Qi. Jiang Ziya (fl. 12th century BC – fl. 11th century BC), also known by several other names, was a Chinese military general, monarch, strategist, and writer who helped kings Wen and Wu of Zhou overthrow the Shang in ancient China. Following their victory at Muye, he continued to serve as a...

 

American economist (1926–2020) This biographical article is written like a résumé. Please help improve it by revising it to be neutral and encyclopedic. (June 2020) James P. QuirkJames Patrick QuirkBorn(1926-11-27)November 27, 1926St. Paul, Minnesota, USDiedJune 4, 2020(2020-06-04) (aged 93)Prescott, Kansas, USAcademic careerAlma materUniversity of Minnesota–MinneapolisDoctoraladvisorLeonid Hurwicz James Patrick Quirk (November 27, 1926 – June 4, 2020) was a Caltech prof...

 

Strategi Solo vs Squad di Free Fire: Cara Menang Mudah!