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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 Cesàro mean, densities of natural numbers and uniform distribution of sequences

M. Blümlinger, N. Obata (1991)

Annales de l'institut Fourier

We are interested in permutations preserving certain distribution properties of sequences. In particular we consider μ -uniformly distributed sequences on a compact metric space X , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of A u t ( N ) leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group 𝒢 . We show that 𝒢 is big in the...

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.

Pointwise limit theorem for a class of unbounded operators in r -spaces

Ryszard Jajte (2007)

Studia Mathematica

We distinguish a class of unbounded operators in r , r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in r -spaces are applied.

Polynomials of multipartitional type and inverse relations

Miloud Mihoubi, Hacène Belbachir (2011)

Discussiones Mathematicae - General Algebra and Applications

Chou, Hsu and Shiue gave some applications of Faà di Bruno's formula to characterize inverse relations. Our aim is to develop some inverse relations connected to the multipartitional type polynomials involving to binomial type sequences.

Product Theorems for Certain Summability Methods in Non-archimedean Fields

P.N. Natarajan (2003)

Annales mathématiques Blaise Pascal

In this paper, K denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in K . The main purpose of this paper is to prove some product theorems involving the methods M and ( N , p n ) in such fields K .

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