Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations

• Autores: David Békollé, Khalil Ezzinbi, Samir Fatajou, Duplex Elvis Houpa Danga, Fritz Mbounja Béssémè
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 1, 2021, págs. 63-85
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000100063
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  • español

    Resumen En este artículo damos condiciones suficientes sobre k ∈ L 1(ℝ) y las medidas positivas µ, ν tales que los espacios de funciones pseudo-casi periódicas que duplican la medida (respectivamente, pseudo-casi automorfas que duplican la medida) son invariantes por el producto de convolución ζf = k ∗ f. Entregamos un ejemplo apropiado para ilustrar nuestros resultados de convolución. Como consecuencia, estudiamos bajo condiciones de Acquistapace-Terreni y dicotomía exponencial, la existencia y unicidad de soluciones (µ, ν)- pseudo-casi periódicas (respectivamente, (µ, ν)- pseudo-casi automorfas) de algunas ecuaciones de evolución parciales no autónomas en espacios de Banach como sistemas neutrales.

  • English

    Abstract In this paper we give sufficient conditions on k ∈ L 1(ℝ) and the positive measures µ, ν such that the doubly-measure pseudo-almost periodic (respectively, doubly-measure pseudo- almost automorphic) function spaces are invariant by the con- volution product ζf = k ∗ f. We provide an appropriate example to illustrate our convolution results. As a conse- quence, we study under Acquistapace-Terreni conditions and exponential dichotomy, the existence and uniqueness of (µ, ν)- pseudo-almost periodic (respectively, (µ, ν)- pseudo-almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces like neutral systems.

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