Değişken üslü Lebesgue uzaylarında konvolüsyonların bazı özellikleri

Abstract

Bu çalışmada değişken üslü Lebesgue uzaylarında konvolüsyon tanımlandı ve Steklov ortalamalarının sonlu lineer birleşimleri ile yaklaşımının mümkün olduğu kanıtlandı. Ayrıca yaklaşım birimi ile oluşturulan özel konvolüsyonlar dizisinin başlangıç fonksiyonuna yakınsadığı gösterildi.

Keywords

• Konvolüsyon
• değişken üslü Lebesgue uzayları
• yaklaşım birimi

Convolutions and approximations in the variable exponent spaces

Abstract

A convolution in the variable exponent Lebesgue spaces is defined and the possibility its approximation by finite linear combinations of Steklov means is proved. Moreover, the convergence of the special convolutions sequence constructed via approximate identity to the original function is showed.

Keywords

• convolution
• variable exponent Lebesgue spaces
• approximate identity

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