Theorems of the same type with greater constants on the right-hand side of (1.1) were proved by Hartman [3] and Koksma [6]. Recently, the author has shown [1] that the theorem of Uchiyama no longer holds if the constant s14 is replaced by any smaller number. Assuming weaker arithmetical restrictions in (1.2) on numerators and denominators of the approximants, the constant in (1.1) can be dimini...

In this paper, we obtain a criterion of boundedness maximal operators associated with smooth hypersurfaces. Also, compute the exact value index such arbitrary convex analytic hypersurfaces in case where Varchenko height hypersurface is greater than two. We for degenerate hypersurfaces, i.e., satisfying assumptions classical Hartman–Nirenberg theorem. The obtained results justify Stein–Iosevich–...

For the two-dimensional nonlinear system \[ u' = a(t) |v|^{1/\alpha} \operatorname{sgn}v, \quad v' - b(t) |u|^{\alpha} \operatorname{sgn}u \] with $\alpha \gt 0$, $a,b \in C[t_{0},\infty)$, $a(t) \geq 0$ ($t t_{0}$), new oscillation criteria and nonoscillation are given in both cases $\int_{t_{0}}^{\infty} a(s) \, ds \infty$ \lt \infty$. One of main results is an analogue Hartman–Wintner theore...

A bounded function φ : G → C on an LCA group G is called Hartman measurable if it can be extended to a Riemann integrable function φ∗ : X → C on some group compactification (ιX , X), i.e. on a compact group X such that ιX : G → X is a continuous homomorphism with image ιX(G) dense in X and φ = φ ∗ ◦ ιX . The concept of Hartman measurability of functions is a generalization of Hartman measurabil...

Marcelo Samuel Berman Editora Albert Einstein Ltda. R. Candido Hartman,575 #17 Ed. Renoir-Champagnat 80730-440 Curitiba PR BRAZIL ABSTRACT New formulae are obtained for the energy of K.N. b.h.’s that point out a gravitomagnetic energy effect. The results are valid for slowly or rapidly rotating black-holes. The expression of the energy density of Kerr-Newman back-holes in the slow rotation case...

In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman i...