Displaying similar documents to “Abstract Korovkin type theorems on modular spaces by 𝒜 -summability”

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.

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...

On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

Igor E. Shparlinski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola a , p ( X , Y ) = ( x , y ) : x y ≡ a ( m o d p ) , 1 ≤ x ≤ X , 1 ≤ y ≤ Y . We give asymptotic formulas for the average values ∑ ( x , y ) ∈ a , p ( X , Y ) x ≠ y * φ ( | x - y | ) / | x - y | and ∑ ( x , y ) ∈ a , p ( X , X ) x ≠ y * φ ( | x - y | ) with the Euler function φ(k) on the differences between the components of points of a , p ( X , Y ) .

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 ) .

Local Indecomposability of Hilbert Modular Galois Representations

Bin Zhao (2014)

Annales de l’institut Fourier

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We prove the indecomposability of the Galois representation restricted to the p -decomposition group attached to a non CM nearly p -ordinary weight two Hilbert modular form over a totally real field F under the assumption that either the degree of F over ℚ is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of F .

On the Nörlund means of Vilenkin-Fourier series

István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)

Czechoslovak Mathematical Journal

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We prove and discuss some new ( H p , L p ) -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients { q k : k ≥ 0 } . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...