A characterization of the space $D^{\prime }_{F}$

S. Pilipović

Displaying similar documents to “A characterization of the space $D_{F}^{'}$ ”

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

Stevan Pilipović (1988)

Annales Polonici Mathematici

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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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One-parameter semigroups in the convolution algebra of rapidly decreasing distributions

(2012)

Colloquium Mathematicae

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The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $_{C}^{'} (ℝ ⁿ; M_{m \times m})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G \in_{C}^{'} (ℝ ⁿ; M_{m \times m})$ is the generating distribution of an i.d.c.s. if and only if the operator $\partial_{t} \otimes_{m \times m} - G *$ on $ℝ^{1 + n}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.

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...

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.

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.

Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor, Kanchan Jain (2011)

Discussiones Mathematicae Probability and Statistics

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For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( $P_{m a x})$ that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine $P_{m a x}$ by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr....

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

Kazimierz Urbanik (1969)

Applicationes Mathematicae

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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.

A note on the spaces of $𝒰^{'}$ type q-dimensional case

S. Pilipović (1981)

Matematički Vesnik

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On the Non-commutative Neutrix Product of $x_{+}^{l} a m b d a$ and $x_{+}^{- l a m b d a - r}$

Brian Fisher, Fatma Al-Sirehy (1999)

Publications de l'Institut Mathématique

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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....

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...

On Fourier asymptotics of a generalized Cantor measure

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)

Colloquium Mathematicae

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Let d be a positive integer and μ a generalized Cantor measure satisfying $μ = \sum_{j = 1}^{m} a_{j} μ \circ S_{j}^{- 1}$ , where $0 < a_{j} < 1$ , $\sum_{j = 1}^{m} a_{j} = 1$ , $S_{j} = ρ R + b_{j}$ with 0 < ρ < 1 and R an orthogonal transformation of $ℝ^{d}$ . Then ⎧1 < p ≤ 2 ⇒ ⎨ $s u p_{r > 0} r^{d (1 / α^{'} - 1 / p^{'})} (\int_{J_{x}^{r}} {| μ ̂ (y) |}^{p^{'}} {d y)}^{1 / p^{'}} \leq D ₁ ρ^{- d / α^{'}}$ , $x \in ℝ^{d}$ , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’ $,$ where $J_{x}^{r} = \prod_{i = 1}^{d} (x_{i} - r / 2, x_{i} + r / 2)$ , α’ is defined by $ρ^{d / α^{'}} = {(\sum_{j = 1}^{m} a_{j}^{p})}^{1 / p}$ and the constants D₁ and D₂ depend only on d and p.

Surjectivity of partial differential operators on ultradistributions of Beurling type in two dimensions

Thomas Kalmes (2010)

Studia Mathematica

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We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions $_{(ω)}^{'} (Ω)$ of Beurling type is equivalent to the surjectivity of P(D) on $C^{\infty} (Ω)$ .

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...

On divisibility of $h^{+}$ by the prime $5$

Stanislav Jakubec (1994)

Mathematica Slovaca

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$E_{1}$ -degeneration and $d^{'} d^{''}$ -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex $(A, d^{'}, d^{''})$ , we show that if it satisfies the $d^{'} d^{''}$ -lemma and the spectral sequence ${E_{r}^{p, q}}$ induced by $A$ does not degenerate at $E_{0}$ , then it degenerates at $E_{1}$ . We apply this result to prove the degeneration at $E_{1}$ of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of $d^{'} d^{''}$ -lemma.

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

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A generalized form of the usual Lognormal distribution, denoted with $_{γ}$ , is introduced through the γ-order Normal distribution $_{γ}$ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $_{γ}$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold $X$ . Then, we define stratified ultradistributions of Beurling and Roumieu type on $X$ . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if $X$ is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to $X$ . Second,...

Displaying similar documents to “A characterization of the space D F ' ”

Displaying similar documents to “A characterization of the space $D_{F}^{'}$ ”