On the asymptotics of counting functions for Ahlfors regular sets

Dušan Pokorný; Marc Rauch

Displaying similar documents to “On the asymptotics of counting functions for Ahlfors regular sets”

Internally club and approachable for larger structures

John Krueger (2008)

Fundamenta Mathematicae

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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

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For a Fuchsian system $d Y / d x = (\sum_{j =}^{p} (A_{j}) / (x - t_{j})) Y$ , (F) $t ₁, t ₂, . . ., t_{p}$ being distinct points in ℂ and $A ₁, A ₂, . . ., A_{p} \in M (n \times n; ℂ)$ , the number α of accessory parameters is determined by the spectral types $s (A ₀), s (A ₁), . . ., s (A_{p})$ , where $A ₀ = - \sum_{j = 1}^{p} A_{j}$ . We call the set $z = (z ₁, z ₂, . . ., z_{α})$ of α parameters a regular coordinate if all entries of the $A_{j}$ are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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When $C_{p} (X)$ is domain representable

William Fleissner, Lynne Yengulalp (2013)

Fundamenta Mathematicae

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Let M be a metrizable group. Let G be a dense subgroup of $M^{X}$ . We prove that if G is domain representable, then $G = M^{X}$ . The following corollaries answer open questions. If X is completely regular and $C_{p} (X)$ is domain representable, then X is discrete. If X is zero-dimensional, T₂, and $C_{p} (X,)$ is subcompact, then X is discrete.

Assertion Q distinguishes topologically ω* and $𝔪$ when $𝔪$ regular and $𝔪 > ω$

R. Frankiewicz (1978)

Colloquium Mathematicae

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$𝒞^{k}$ -regularity for the $\bar{\partial}$ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let $D$ be a $𝒞^{d}$ $q$ -convex intersection, $d \geq 2$ , $0 \leq q \leq n - 1$ , in a complex manifold $X$ of complex dimension $n$ , $n \geq 2$ , and let $E$ be a holomorphic vector bundle of rank $N$ over $X$ . In this paper, $𝒞^{k}$ -estimates, $k = 2, 3, \dots, \infty$ , for solutions to the $\bar{\partial}$ -equation with small loss of smoothness are obtained for $E$ -valued $(0, s)$ -forms on $D$ when $n - q \leq s \leq n$ . In addition, we solve the $\bar{\partial}$ -equation with a support condition in $𝒞^{k}$ -spaces. More precisely, we prove that for a $\bar{\partial}$ -closed form $f$ in $𝒞_{0, q}^{k} (X ∖ D, E)$ , $1 \leq q \leq n - 2$ , $n \geq 3$ , with compact support and for $ε$ with $0 < ε < 1$ there...

On the $n$ -fold symmetric product of a space with a $σ$ - $(P)$ -property $c n$ -network ( $c k$ -network)

Luong Q. Tuyen, Ong V. Tuyen (2020)

Commentationes Mathematicae Universitatis Carolinae

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We study the relation between a space $X$ satisfying certain generalized metric properties and its $n$ -fold symmetric product $ℱ_{n} (X)$ satisfying the same properties. We prove that $X$ has a $σ$ - $(P)$ -property $c n$ -network if and only if so does $ℱ_{n} (X)$ . Moreover, if $X$ is regular then $X$ has a $σ$ - $(P)$ -property $c k$ -network if and only if so does $ℱ_{n} (X)$ . By these results, we obtain that $X$ is strict $σ$ -space (strict $ℵ$ -space) if and only if so is $ℱ_{n} (X)$ .

The general rigidity result for bundles of $A$ -covelocities and $A$ -jets

Jiří M. Tomáš (2017)

Czechoslovak Mathematical Journal

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Let $M$ be an $m$ -dimensional manifold and $A = 𝔻_{k}^{r} / I = ℝ \oplus N_{A}$ a Weil algebra of height $r$ . We prove that any $A$ -covelocity $T_{x}^{A} f \in T_{x}^{A *} M$ , $x \in M$ is determined by its values over arbitrary $max {width A, m}$ regular and under the first jet projection linearly independent elements of $T_{x}^{A} M$ . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result $T^{A *} M ≃ T^{r *} M$ without coordinate computations, which improves and generalizes the partial...

Coloring Cantor sets and resolvability of pseudocompact spaces

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let us denote by $Φ (λ, μ)$ the statement that $𝔹 (λ) = D {(λ)}^{ω}$ , i.e. the Baire space of weight $λ$ , has a coloring with $μ$ colors such that every homeomorphic copy of the Cantor set $ℂ$ in $𝔹 (λ)$ picks up all the $μ$ colors. We call a space $X$ $π$ -regular if it is Hausdorff and for every nonempty open set $U$ in $X$ there is a nonempty open set $V$ such that $\bar{V} \subset U$ . We recall that a space $X$ is called feebly compact if every locally finite collection of open sets in $X$ is finite. A Tychonov space is pseudocompact if and...