arXiv subjects
Publications and source records attributed to Alexey Pyshkin.
In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong tridiagonal $M$-basis that was not rank one dense. Later Katavolos, Lambrou and Papadakis studied $k$ point density property of this example. In this paper we present new methods for the analysis of $k$ point density and rank one density properties for band-diagonal $M$-bases.
In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong $M$-basis that did not admit a linear summation method. We study a class of $M$-bases $\mathfrak{F}=\{f_n\}_{n=1}^\infty$ in the Hilbert space that generalizes the Larson--Wogen system. We determine the conditions under which $\mathfrak{F}$ admits a linear summation method. In order to do that we employ some of the graph theory techniques.