On an Application of Parseval's Formula to Problems of $G_\theta^\varkappa$-summability of Eigenfunction Expansion of the Laplacian Operator
DOI:
https://doi.org/10.5644/SJM.12.2.12Keywords:
Eigenfunction expansion, $G_\theta^\varkappa$-summabilityAbstract
To the memory of deeply respected Academician Mahmut Bajraktarević
In this paper, applying Parseval's formula, we prove a $G_\theta^\varkappa$–summability analogue of Avadhani's theorem for the Riesz–summability of the eigenfunction expansion. A crucial step in our proof of this theorem was to find a function $g(x)$ that would lead us to the kernel of the $G_\theta^\varkappa$–summability, which is more complex than the kernel of the Riesz –
summability.
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