On the asymptotic behaviour of the $G_\theta^{\k}$-means of eigenfunction expansion related to the slowly oscillating functions with remainder term

Manojlo Maravi\'c

Abstract: Let $f(Q)=f(x_1,\ldots,x_n)\in L^2(D)$ where $D$ is a bounded open domain with a sufficiently regular boundary in the space $E^n$. Two theorems are proved in this paper. The main result is expressed by Theorem 2 which connects the asymptotic behaviour of the $G_\theta^\kappa $ means of eigenfunction expansion $(2.1)$ with the behaviour of the spherical mean of function $f$ when this is related to behaviour of a slowly oscillating function with remainder term.

Classification (MSC2000): 42C99

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