Displaying similar documents to “Summability of first integrals of a C ω -non-integrable resonant Hamiltonian system”

On generalized absolute Cesaro summability factors

A. Nihal Tuncer (2002)

Annales Polonici Mathematici

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Using δ-quasi-monotone and any almost increasing sequences we prove a theorem on | C , α , β ; δ | k summability factors of infinite series, which generalizes a theorem of Mazhar [7] on | C , 1 | k summability factors.

Translativity of absolute weighted mean summability

Cihan Orhan (1998)

Czechoslovak Mathematical Journal

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In this paper, we give necessary and sufficient conditions on ( p n ) for | R , p n | k , k ≥ 1 , to be translative. So we extend the known results of Al-Madi [1] and Cesco 4 to the case k > 1 .

Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences

Ferenc Móricz (2013)

Studia Mathematica

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Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that l i m t → ∞ τ ( t ) = A , where τ ( t ) : = 1 / ( l o g t ) ∫ 1 t s ( u ) / u d u . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function...

Borel summable solutions of the Burgers equation

Grzegorz Łysik (2009)

Annales Polonici Mathematici

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We give necessary and sufficient conditions for the formal power series solutions to the initial value problem for the Burgers equation ∂ t u - ∂ x ² u = ∂ x ( u ² ) to be convergent or Borel summable.

Power means and the reverse Hölder inequality

Victor D. Didenko, Anatolii A. Korenovskyi (2011)

Studia Mathematica

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Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means α w ( x ) : = ( ( 1 / x ) ∫ 0 x w α ( t ) d t ) 1 / α , x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.

Multi-dimensional Fejér summability and local Hardy spaces

Ferenc Weisz (2009)

Studia Mathematica

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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space W ( h p , ℓ ∞ ) to W ( L p , ℓ ∞ ) . This implies the almost everywhere convergence of the Fejér means in a cone for all f ∈ W ( L ₁ , ℓ ∞ ) , which is larger than L ₁ ( ℝ d ) .

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

Ryszard Jajte (2007)

Studia Mathematica

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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.