Metric transitivity and integer valued functions

Solomon Schwartzman

Displaying similar documents to “Metric transitivity and integer valued functions”

On $p$ -adic Euler constants

Abhishek Bharadwaj (2021)

Czechoslovak Mathematical Journal

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The goal of this article is to associate a $p$ -adic analytic function to the Euler constants $γ_{p} (a, F)$ , study the properties of these functions in the neighborhood of $s = 1$ and introduce a $p$ -adic analogue of the infinite sum $\sum_{n \geq 1} f (n) / n$ for an algebraic valued, periodic function $f$ . After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to $p$ -adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove...

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

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We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p} (μ, X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p} (μ, X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological...

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

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Let $K \subset ℝ^{m}$ ( $m \geq 2$ ) be a compact set; assume that each ball centered on the boundary $B$ of $K$ meets $K$ in a set of positive Lebesgue measure. Let $C_{0}^{(1)}$ be the class of all continuously differentiable real-valued functions with compact support in $ℝ^{m}$ and denote by $σ_{m}$ the area of the unit sphere in $ℝ^{m}$ . With each $ϕ \in C_{0}^{(1)}$ we associate the function $W_{K} ϕ (z) = \frac{1}{σ_{m}} \underset{ℝ^{m} ∖ K}{\to} \int g r a d ϕ (x) \cdot \frac{z - x}{{| z - x |}^{m}} x$ of the variable $z \in K$ (which is continuous in $K$ and harmonic in $K ∖ B$ ). $W_{K} ϕ$ depends only on the restriction ${ϕ |}_{B}$ of $ϕ$ to the boundary $B$ of $K$ . This gives rise to a linear operator $W_{K}$ ...

On the quasi-periodic $p$ -adic Ruban continued fractions

Basma Ammous, Nour Ben Mahmoud, Mohamed Hbaib (2022)

Czechoslovak Mathematical Journal

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We study a family of quasi periodic $p$ -adic Ruban continued fractions in the $p$ -adic field $ℚ_{p}$ and we give a criterion of a quadratic or transcendental $p$ -adic number which based on the $p$ -adic version of the subspace theorem due to Schlickewei.

The max norm in $R^{n}$ -isometries and measure

Regina Cohen, James W. Fickett (1982)

Colloquium Mathematicae

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A remark on a lower envelope principle

Masanori Kishi (1964)

Annales de l'institut Fourier

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Soit $Ω$ un espace topologique localement séparé et soit $G$ un noyau (symétrique ou non) positif et continu au sens large dans $Ω$ . Si $G$ satisfait au principe de domination ordinaire et si le noyau adjoint $\overset{ˇ}{G}$ est régulier, alors $X$ satisfait au principe de l’enveloppe inférieure sur tout compact, c’est-à-dire, pour tout compact $K \subset Ω$ et toutes mesures positives $μ$ et $ν$ (l’une d’elles d’énergie finie), il existe une mesure positive $λ$ portée par $K$ telle que $G λ = G μ \land G ν$ à p.p.p. sur $K$ . Ici nous considérons le...

A limit involving functions in $W_{0}^{1, p} (Ω)$

Biagio Ricceri (1999)

Colloquium Mathematicae

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We point out the following fact: if Ω ⊂ $ℝ^{n}$ is a bounded open set, δ>0, and p>1, then $l i m_{\to 0^{+}} i n f_{\in V} \int_{Ω} {| \nabla (x) |}^{p} d x = \infty$ , where $V_{=} \in W_{0}^{1, p} (Ω) : m e a s (x \in Ω : | (x) | > δ) > .$

Relations between Shy Sets and Sets of $ν_{p}$ -Measure Zero in Solovay’s Model

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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An example of a non-zero non-atomic translation-invariant Borel measure $ν_{p}$ on the Banach space $ℓ_{p} (1 \leq p \leq \infty)$ is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition " $ν_{p}$ -almost every element of $ℓ_{p}$ has a property P" implies that “almost every” element of $ℓ_{p}$ (in the sense of [4]) has the property P. It is also shown that the converse is not valid.

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier

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It is known that with a non-unit Pisot substitution $σ$ one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional...