A convergence theory of some methods of integration.
Addendum to the paper "Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅ ²₊" (Studia Math. 201 (2010), 287-304)
Développement asymptotique d'intégrales oscillantes lentement convergentes à l'infini
Generalizations of the Riemann-Lebesgue and Cantor-Lebesgue lemmas
Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅²₊
We investigate the convergence behavior of the family of double sine integrals of the form , where (u,v) ∈ ℝ²₊:= ℝ₊ × ℝ₊, ℝ₊:= (0,∞), and f: ℝ²₊ → ℂ is a locally absolutely continuous function satisfying certain generalized monotonicity conditions. We give sufficient conditions for the uniform convergence of the remainder integrals to zero in (u,v) ∈ ℝ²₊ as maxa₁,a₂ → ∞ and , j = 1,2 (called uniform convergence in the regular sense). This implies the uniform convergence of the partial integrals...
Integrability theorems for power series
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
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 , where . (*) 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 s is slowly...
On a class of sequences defined by using Riemann integral.
On some conditions for the almost everywhere convergence of a class of integrable functions
On some properties of multiple moduli of continuity.
Some remarks on -faster convergent infinite series
A structure of terms of -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of -faster convergent series with different types of their terms are proved. Some consequences are discussed.
The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.
Zur Theorie der bestimmten Integrale und der unendlichen Reihen
О нахождении производящих функций и комбинаторных сумм с помощью многомерных вычетов
Об абсолютной сходимости интеграла Фурье на плоскости.