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13 results on '"Normability"'

1. On Local Normability of Spaces of Keplerian Orbits.

Author

Milanov, D. V.

Abstract

Geometric properties of spaces of Keplerian orbits are of interest for celestial mechanics problems related to the search for groups of celestial bodies with close orbits. Those groups include asteroid families and meteor streams. Studying these groups provides important information on the evolution of the Solar System, as well as on the characteristics of objects within a family and their parent bodies. The local properties of a distance function between orbits are of primary importance for the problems of the search for families of related celestial bodies, because orbits of family members cluster together in a small region of the orbit space. Several metrics on the set of Keplerian orbits and its quotient sets are considered in this paper. For each of these metrics we solve the question: is there a normed vector space that is locally isometric to the orbit metric space? In two of the considered cases, the answer turns out to be positive: the quotient space of by the equivalence relation neglecting the magnitude of the pericenter argument of the orbit can be isometrically embedded into . The embedding into also exists for the quotient space by the pair of elements: the longitude of ascending node and the pericenter argument. It is shown in this paper that for other metrics, the answer to the stated question is negative. The possibility of an isometric embedding of the orbit space or its part into Euclidean space is useful in application to the aforementioned problems of celestial mechanics. The isometric map helps to define the mean of the orbit family in a natural way: the arithmetic mean of images corresponds to the orbit with the minimum square deviation of distances from the orbits of the family. [ABSTRACT FROM AUTHOR]

Published
2019
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3. Convex sets in modules over semifields.

Author

Biebler, Karl-Ernst

Subjects
*CONVEX sets, *MODULES (Algebra), *MULTIPLICATION, *LINEAR systems, *TOPOLOGICAL spaces, *TOPOLOGICAL groups
Abstract

Semifields are commutative preordered rings for which a weak invertibility of the multiplication is defined. Examples are the Stone algebras and the extended complete vector lattices. Convex sets, strong convex sets and absolute convex sets are defined and studied in semifield modules. This is applied to investigations concerning the problem of the semifield-normability of semifield-lineartopological semifield-modules. [ABSTRACT FROM AUTHOR]

Published
2015
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4. Normability via the Convergence of Closed and Convex Sets.

Author

Dancs, S., Medvegyev, P., and Magyarkuti, Gy.

Subjects
*VECTOR topology, *STOCHASTIC convergence, *CONVEX sets, *HAUSDORFF measures, *INTERSECTION theory
Abstract

The purpose of this short technical note is to show that a locally convex topological vector space is normable, if and only if an important convergence theorem about closed and convex sets holds. This new assumption of normability is related to the problem of preservation of Hausdorff lower continuity of the intersection of Hausdorff lower continuous, closed and convex valued correspondences. [ABSTRACT FROM AUTHOR]

Published
2011
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6. On the normability of generalized Šerstnev PN spaces

Author

Zhang, Gaoxun and Zhang, Minxian

Subjects
*KOLMOGOROV complexity, *DISTRIBUTION (Probability theory), *COMPLEX variables, *MATHEMATICAL analysis
Abstract

Abstract: Probabilistic Normed spaces have been redefined by C. Alsina, B. Schweizer and A. Sklar. But even today, whether the generalized Šerstnev PN space is normable or not is still an open question. In this paper, through applying Kolmogorov''s theorem, we will give several sufficient conditions, under which many generalized Šerstnev PN spaces are normable. As the application of our results, we will give two examples which are normable generalized Šerstnev PN space, but not Šerstnev space. [Copyright &y& Elsevier]

Published
2008
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7. On the normability of Marcinkiewicz classes.

Author

Astashkin, S.

Subjects
*NUMERICAL analysis, *INTERPOLATION, *APPROXIMATION theory, *BLOWING up (Algebraic geometry), *OPERATOR theory, *ASYMPTOTIC expansions
Abstract

We obtain simple necessary and sufficient conditions for the normability of Marcinkiewicz classes, which play an important role in various problems of analysis. These conditions are stated in terms of dilation exponents of the function generating the given class as well as in terms of interpolation for operators bounded in the couple ( L 1, L ∞). [ABSTRACT FROM AUTHOR]

Published
2007
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8. Functional properties of rearrangement invariant spaces defined in terms of oscillations

Author

Carro, María J., Gogatishvili, Amiran, Martín, Joaquim, and Pick, Luboš

Subjects
*LEBESGUE integral, *FUNCTIONAL analysis, *WEIGHTS & measures, *OSCILLATIONS
Abstract

Abstract: Function spaces whose definition involves the quantity , which measures the oscillation of , have recently attracted plenty of interest and proved to have many applications in various, quite diverse fields. Primary role is played by the spaces , with and a weight function on , defined as the set of Lebesgue-measurable functions on such that andSome of the main open questions concerning these spaces relate to their functional properties, such as their lattice property, normability and linearity. We study these properties in this paper. [Copyright &y& Elsevier]

Published
2005
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9. Váhové prostory funkcí invariantní vůči přerovnání a jejich základní vlastnosti

Author

Soudský, Filip, Pick, Luboš, Soria, Javier, and Barza, Sorina

Subjects
Weight, vnoření, Váha, Banach function space, Embedding, Banachův prostor funkcí, normovatelnost, Normability
Abstract

In this thesis we shall provide the reader with results in the field of classical Lorentz spaces. These spaces have been studied since the 50's and have many applications in partial differential equations and interpolation theory. This work includes five papers. First paper studies the properties of Generalized Gamma spaces. Second paper provides an alternative proof of normability characterization of classical Lorentz spaces. The third paper discus conditions of linearity and quasi-norm property of rearrangement-invariant lattices. The following paper gives a characterization of normability of Gamma spaces. And finally the last paper characterizes the embeddings between Generalized Gamma spaces. Powered by TCPDF (www.tcpdf.org)

Published
2017

10. Functional properties of rearrangement invariant spaces defined in terms of oscillations

Author

Luboš Pick, María J. Carro, Joaquim Martín, and Amiran Gogatishvili

Subjects
Discrete mathematics, Lattice property, Weight function, Distribution function, Decreasing rearrangement, Oscillation, Invariant (mathematics), Normability, Analysis, Mathematics, Abstract function
Abstract

Function spaces whose definition involves the quantity f * * - f * , which measures the oscillation of f * , have recently attracted plenty of interest and proved to have many applications in various, quite diverse fields. Primary role is played by the spaces S p ( w ) , with 0 p ∞ and w a weight function on ( 0 , ∞ ) , defined as the set of Lebesgue-measurable functions on R such that f * ( ∞ ) = 0 and ∥ f ∥ S p ( w ) := ∫ 0 ∞ ( f * * ( s ) - f * ( s ) ) p w ( s ) ds 1 / p ∞ . Some of the main open questions concerning these spaces relate to their functional properties, such as their lattice property, normability and linearity. We study these properties in this paper.

Published
2005

11. Normability of Probabilistic Normed Spaces

Author

Lafuerza Guillén, Bernardo, Rodríguez-Lallena, José Antonio, Sempi, Carlo, B., LAFUERZA GUILLEN, J. A., RODRIGUEZ LALLENA, and Sempi, Carlo

Subjects
Mathematics::Functional Analysis, Probabilistic Normed Spaces, Probability (math.PR), General Topology (math.GN), 54E70, 46S50, Mathematics::General Topology, t-norm, topologically bounded set, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, $\mathcal{D}$-bounded set, probabilistic radiu, normability, \v{S}erstnev space, Matematica, Mathematics - Probability, probabilistic normed space, Mathematics - General Topology
Abstract

Relying on Kolmogorov's classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normable \v{S}erstnev spaces. We also study the normability of other two classes of Probabilistic Normed Spaces., Comment: 8 pages

Published
2004
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12. On the normability of generalized Šerstnev PN spaces

Author

Minxian Zhang and Gaoxun Zhang

Subjects
Algebra, Applied Mathematics, Probabilistic logic, Topologically bounded, Space (mathematics), Locally convex, Normability, Analysis, Mathematics
Abstract

Probabilistic Normed spaces have been redefined by C. Alsina, B. Schweizer and A. Sklar. But even today, whether the generalized Šerstnev PN space is normable or not is still an open question. In this paper, through applying Kolmogorov's theorem, we will give several sufficient conditions, under which many generalized Šerstnev PN spaces are normable. As the application of our results, we will give two examples which are normable generalized Šerstnev PN space, but not Šerstnev space.

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