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Schur multiplier characterization of a class of infinite matrices

A. Marcoci, L. Marcoci, L. E. Persson, N. Popa (2010)

Czechoslovak Mathematical Journal

Let B w ( p ) denote the space of infinite matrices A for which A ( x ) p for all x = { x k } k = 1 p with | x k | 0 . We characterize the upper triangular positive matrices from B w ( p ) , 1 < p < , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

Second order linear q -difference equations: nonoscillation and asymptotics

Pavel Řehák (2011)

Czechoslovak Mathematical Journal

The paper can be understood as a completion of the q -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear q -difference equations. The q -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice q 0 : = { q k : k 0 } with q > 1 . In addition to recalling the existing concepts of q -regular variation and q -rapid variation we introduce q -regularly bounded functions and prove many related properties. The q -Karamata theory is then...

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