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On the asymptotic behaviour of the \(G^ k_{\theta}\)-means of eigenfunction expansion related to the slowly oscillating functions with remainder term. (English) Zbl 0704.42029

Summary: Let \(f(Q)=f(x_ 1,...,x_ n)\in L^ 2(D)\) where D is a bounded open domain with the 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 \(G^ k_{\theta}\) means of a given eigenfunction expansion with the behaviour of the spherical mean of function f when this is related to behaviour of a slowly oscillating function with remainder term.

MSC:

42C99 Nontrigonometric harmonic analysis
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