Remarks on absolutely regular and regular $K^{\prime }{M_p}$-distributions

S. Pilipović

Displaying similar documents to “Remarks on absolutely regular and regular $K^{'} M_{p}$ -distributions”

On regular $K^{'} M_{P}$ -distributions

Stevan Pilipović (1988)

Annales Polonici Mathematici

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

V. Swaminathan (1977)

Matematički Vesnik

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Inequalities for a regular polygon in $L^{p}$ spaces

M. Pavlović (1992)

Matematički Vesnik

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Unit-regularity and representability for semiartinian $*$ -regular rings

Christian Herrmann (2020)

Archivum Mathematicum

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We show that any semiartinian $*$ -regular ring $R$ is unit-regular; if, in addition, $R$ is subdirectly irreducible then it admits a representation within some inner product space.

The genera, reflexibility and simplicity of regular maps

Marston Conder, Jozef Širáň, Thomas Tucker (2010)

Journal of the European Mathematical Society

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This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to $g - 1$ , where $g$ is the genus, all orientably-regular maps of genus $p + 1$ for $p$ prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and...

Universal completely regular dendrites

K. Omiljanowski, S. Zafiridou (2005)

Colloquium Mathematicae

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We define a dendrite $E_{n}$ which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite $E_{ω}$ is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite $D_{n}$ of order n described by J. J. Charatonik.

Kernel theorems in spaces of generalized functions

Antoine Delcroix (2010)

Banach Center Publications

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In analogy to the classical isomorphism between ((ℝⁿ), $^{'} (ℝ^{m}))$ and $^{'} (ℝ^{m + n})$ (resp. $((ℝ ⁿ),^{'} (ℝ^{m}))$ and $^{'} (ℝ^{m + n})$ ), we show that a large class of moderate linear mappings acting between the space $_{C} (ℝ ⁿ)$ of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space $_{} (ℝ ⁿ)$ of Colombeau rapidly decreasing generalized functions and the space $_{τ} (ℝ ⁿ)$ of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of $(ℝ^{m + n})$ (resp. $_{τ} (ℝ^{m + n})$ ). The main novelty is to use...

On the asymptotics of counting functions for Ahlfors regular sets

Dušan Pokorný, Marc Rauch (2022)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the so-called Ahlfors regular sets (also known as $s$ -regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit ${lim}_{ε \to 0 +} ε^{s} N (ε, K)$ exist, where $K$ is an $s$ -regular set and $N (ε, K)$ is for instance the $ε$ -packing number of $K$ ?

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.

On $C_{0 \cdot}$ multi-contractions having a regular dilation

Dan Popovici (2005)

Studia Mathematica

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Commuting multi-contractions of class $C_{0 \cdot}$ and having a regular isometric dilation are studied. We prove that a polydisc contraction of class $C_{0 \cdot}$ is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence. ...

A characterization of the space $D_{F}^{'}$

S. Pilipović (1982)

Matematički Vesnik

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On the distribution of prime numbers which are of the form $x^{2} + y^{2} + 1$

Yoichi Motohashi (1970)

Acta Arithmetica

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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...

Equicontinuity and Convergent Sequences in the Spaces $_{C}^{'}$ and $_{M}$

Jan Kisyński (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Characterizations of equicontinuity and convergent sequences are given for the space $_{C}^{'} (ℝ ⁿ)$ of rapidly decreasing distributions and the space $_{M} (ℝ ⁿ)$ of slowly increasing infinitely differentiable functions.

Comaximal graph of $C (X)$

Mehdi Badie (2016)

Commentationes Mathematicae Universitatis Carolinae

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In this article we study the comaximal graph $Γ_{_{2}}^{'} C (X)$ of the ring $C (X)$ . We have tried to associate the graph properties of $Γ_{_{2}}^{'} C (X)$ , the ring properties of $C (X)$ and the topological properties of $X$ . Radius, girth, dominating number and clique number of the $Γ_{_{2}}^{'} C (X)$ are investigated. We have shown that $2 \leq Rad Γ_{_{2}}^{'} C (X) \leq 3$ and if $| X | > 2$ then $girth Γ_{_{2}}^{'} C (X) = 3$ . We give some topological properties of $X$ equivalent to graph properties of $Γ_{_{2}}^{'} C (X)$ . Finally we have proved that $X$ is an almost $P$ -space which does not have isolated points if and only if $C (X)$ is an almost...

Bigraphic pairs with a realization containing a split bipartite-graph

Jian Hua Yin, Jia-Yun Li, Jin-Zhi Du, Hai-Yan Li (2019)

Czechoslovak Mathematical Journal

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Let $K_{s, t}$ be the complete bipartite graph with partite sets ${x_{1}, ..., x_{s}}$ and ${y_{1}, ..., y_{t}}$ . A split bipartite-graph on $(s + s^{'}) + (t + t^{'})$ vertices, denoted by ${SB}_{s + s^{'}, t + t^{'}}$ , is the graph obtained from $K_{s, t}$ by adding $s^{'} + t^{'}$ new vertices $x_{s + 1}, ..., x_{s + s^{'}}$ , $y_{t + 1}, ..., y_{t + t^{'}}$ such that each of $x_{s + 1}, ..., x_{s + s^{'}}$ is adjacent to each of $y_{1}, ..., y_{t}$ and each of $y_{t + 1}, ..., y_{t + t^{'}}$ is adjacent to each of $x_{1}, ..., x_{s}$ . Let $A$ and $B$ be nonincreasing lists of nonnegative integers, having lengths $m$ and $n$ , respectively. The pair $(A; B)$ is potentially ${SB}_{s + s^{'}, t + t^{'}}$ -bigraphic if there is a simple bipartite graph containing ${SB}_{s + s^{'}, t + t^{'}}$ (with $s + s^{'}$ vertices $x_{1}, ..., x_{s + s^{'}}$ in the part of size $m$ ...

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

R. Frankiewicz (1978)

Colloquium Mathematicae

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Duality of matrix-weighted Besov spaces

Svetlana Roudenko (2004)

Studia Mathematica

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We determine the duals of the homogeneous matrix-weighted Besov spaces $Ḃ_{p}^{α q} (W)$ and $ḃ_{p}^{α q} (W)$ which were previously defined in [5]. If W is a matrix $A_{p}$ weight, then the dual of $Ḃ_{p}^{α q} (W)$ can be identified with $Ḃ_{p^{'}}^{- α q^{'}} (W^{- p^{'} / p})$ and, similarly, $[ḃ_{p}^{α q} (W)] * \approx ḃ_{p^{'}}^{- α q^{'}} (W^{- p^{'} / p})$ . Moreover, for certain W which may not be in the $A_{p}$ class, the duals of $Ḃ_{p}^{α q} (W)$ and $ḃ_{p}^{α q} (W)$ are determined and expressed in terms of the Besov spaces $Ḃ_{p^{'}}^{- α q^{'}} (A_{Q}^{- 1})$ and $ḃ_{p^{'}}^{- α q^{'}} (A_{Q}^{- 1})$ , which we define in terms of reducing operators ${A_{Q}}_{Q}$ associated with W. We also develop the basic theory of these reducing operator Besov spaces....

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for $S^{1}$ -valued maps $m^{'}$ (the magnetization) of two variables $x^{'}$ : $E_{ε} (m^{'}) = ε \int {| \nabla^{'} \cdot m^{'} |}^{2} d x^{'} + \frac{1}{2} \int {|| \nabla^{'} |^{- 1 / 2} \nabla^{'} \cdot m^{'}|}^{2} d x^{'}$ . We are interested in the behavior of minimizers as $ε \to 0$ . They are expected to be $S^{1}$ -valued maps $m^{'}$ of vanishing distributional divergence $\nabla^{'} \cdot m^{'} = 0$ , so that appropriate boundary conditions enforce line discontinuities. For finite $ε > 0$ , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

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We consider elementary operators $x \mapsto \sum_{j = 1}^{n} a_{j} x b_{j}$ , acting on a unital Banach algebra, where $a_{j}$ and $b_{j}$ are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families $a_{j}$ and $b_{j}$ , i.e. $a_{j} = a_{j}^{'} + i a_{j}^{''}$ ( $b_{j} = b_{j}^{'} + i b_{j}^{''}$ ), where all $a_{j}^{'}$ and $a_{j}^{''}$ ( $b_{j}^{'}$ and $b_{j}^{''}$ ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...

Displaying similar documents to “Remarks on absolutely regular and regular K ' M p -distributions”

Displaying similar documents to “Remarks on absolutely regular and regular $K^{'} M_{p}$ -distributions”