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p-Analytic and p-quasi-analytic vectors

Jan Rusinek (1998)

Studia Mathematica

For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.

Permutations preserving sums of rearranged real series

Roman Wituła (2013)

Open Mathematics

The aim of this paper is to discuss one of the most interesting and unsolved problems of the real series theory: rearrangements that preserve sums of series. Certain hypothesis about combinatorial description of the corresponding permutations is presented and basic algebraic properties of the family 𝔖 0 , introduced by it, are investigated.

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