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This subtopic studies matrix methods of summability, where linear transformations of sequences are used to regularize or compare different convergence notions.
40C05 develops matrix methods for summability in matrix methods of summability. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Matrix methods for summability
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40C10 develops matrix methods in summability of sequences and series of functions in matrix methods of summability. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Wikipedia search: Matrix methods in summability of sequences and series of functions
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
40C15 develops function-theoretic methods (including power series methods and semicontinuous methods) in matrix methods of summability. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.