Loading...
Publication
Equações integrais de Sonine
| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 4.4 MB | Adobe PDF |
Authors
Advisor(s)
Abstract(s)
As equações integrais de Sonine são equações de primeira espécie, de Volterra,
Kfp =f , com núcleo às diferenças, tais que existe um núcleo associado ao núcleo original de modo que sejam ambos divisores da unidade para a convolução.
No Capitulo I realiza-se a inversão do operador K no quadro dos espaços Lp(R) e obtêm-se as condições necessárias e suficientes para que uma função pertença ao contradomínio deste operador. Este resultado é conseguido após investigação das propriedades dos núcleos de Sonine e das condições especiais exigidas para a construção da forma de Marchaud do operador inverso. O contradomínio do operador K é descrito como subconjunto de um espaço de Orlicz.
No Capitulo ll efectua-se a inversão do operador K no quadro dos espaços Lp(0,b). A inversão é natural evitando hipóteses que envolvam condições no infinito.
No Capitulo lll estuda-se uma relação entre os operadores de Sonine esquerdo e direito, a qual permite considerar algumas equações integrais generalizadas do tipo de Sonine.
No Capitulo IV estabelece-se a existência de isomorfismos entre espaços de Hölder generalizados, com e sem ponderação. Estes resultados exigem o estudo da limitação dos operadores K e K-1 nestes espaços.
Sonine integral equations are Volterra first kind integral equations Kp =f with a difference kernel such that there exists another kernel associated with the original kernel so that both are unit divisors for the convolution. In Chapter I the operator K is inverted in the frame of spaces Lp(R) and necessary and sufficient conditions are obtained for a function to belong to the range of K . This result is obtained after an investigation of Sonine kernels properties and of the special conditions required to construct the Marchaud representation of K-1. The range of the operator K is described as a subset of an Orlicz space . In Chapter ll the inversion of operator K is attained in the frame of spaces Lp([0,b]). The inversion is natural being related to the kernel values in [0,b] and avoiding conditions at infinity. In Chapter Ill a relation between the left-hand sided and right-hand sided Sonine operators is studied, which allows considering of some generalized Sonine-type integral equations. Chapter IV establishes the existence of isomorphisms between generalized Hölder spaces, weighted and non-weighted. These results require the study of the boundedness of operators K and K-1 in these spaces.
Sonine integral equations are Volterra first kind integral equations Kp =f with a difference kernel such that there exists another kernel associated with the original kernel so that both are unit divisors for the convolution. In Chapter I the operator K is inverted in the frame of spaces Lp(R) and necessary and sufficient conditions are obtained for a function to belong to the range of K . This result is obtained after an investigation of Sonine kernels properties and of the special conditions required to construct the Marchaud representation of K-1. The range of the operator K is described as a subset of an Orlicz space . In Chapter ll the inversion of operator K is attained in the frame of spaces Lp([0,b]). The inversion is natural being related to the kernel values in [0,b] and avoiding conditions at infinity. In Chapter Ill a relation between the left-hand sided and right-hand sided Sonine operators is studied, which allows considering of some generalized Sonine-type integral equations. Chapter IV establishes the existence of isomorphisms between generalized Hölder spaces, weighted and non-weighted. These results require the study of the boundedness of operators K and K-1 in these spaces.
Description
Keywords
Equações integrais Núcleos de Sonine Integrais e derivadas fraccionários Módulo de continuidade espaços de Hölder generalizados