On regular $K^{\prime }{M_P}$-distributions

Stevan Pilipović

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Displaying similar documents to “On regular $K^{'} M_{P}$ -distributions”

Remarks on absolutely regular and regular $K^{'} M_{p}$ -distributions

S. Pilipović (1991)

Annales Polonici Mathematici

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nbspAbstract. We give the definition of $K^{'} M_{P}$ regular distributions and some characterizations of absolutely regular and regular $K^{'} M_{p}$ -distributions.

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

S. Pilipović (1982)

Matematički Vesnik

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

V. Swaminathan (1977)

Matematički Vesnik

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

Yoichi Motohashi (1970)

Acta Arithmetica

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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.

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.

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 $K$ ?

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

M. Pavlović (1992)

Matematički Vesnik

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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.

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...

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 the Cauchy problem for convolution equations

(2013)

Colloquium Mathematicae

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We consider one-parameter (C₀)-semigroups of operators in the space $^{'} (ℝ ⁿ; ℂ^{m})$ with infinitesimal generator of the form ${(G *) |}_{^{'} (ℝ ⁿ; ℂ^{m})}$ where G is an $M_{m \times m}$ -valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces $(ℝ ⁿ; ℂ^{m})$ , $_{L^{p}} (ℝ ⁿ; ℂ^{m})$ , p ∈ [1,∞], $(_{a}) (ℝ ⁿ; ℂ^{m})$ , a ∈ ]0,∞[, or the spaces $_{L^{q}}^{'} (ℝ ⁿ; ℂ^{m})$ , q ∈ ]1,∞], of bounded distributions.

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. ...

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...

Self-decomposable probability distributions on $R^{m}$

Kazimierz Urbanik (1969)

Applicationes Mathematicae

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

R. Frankiewicz (1978)

Colloquium Mathematicae

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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...

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....

Displaying similar documents to “On regular K ' M P -distributions”

Displaying similar documents to “On regular $K^{'} M_{P}$ -distributions”