Showing papers on "Space (mathematics) published in 1983"
Book•
01 Jan 1983
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Abstract: How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.
4,099 citations
Book•
01 Nov 1983
TL;DR: In this paper, a family of modulars depending on a parameter is described, and some applications of modular spaces are discussed, including orlicz spaces and countably modulared spaces.
Abstract: Modular spaces.- Orlicz spaces.- Countably modulared spaces.- Families of modulars depending on a parameter.- Some applications of modular spaces.
1,732 citations
TL;DR: In this article, the authors introduced the notion of an approximation apace as the pair A = (U,R), where U denotes an a rb i t ry non-empty set and S denotes some equivalence r e l a t i o n on U, and the best upper approximation of X in A is defined by AX.
Abstract: Introduction In [l] Z. Pawlak introduced the notion of an approximation apace as the pair A = (U,R), where U denotes an a rb i t ra ry non-empty set and S denotes some equivalence r e l a t i o n on U, ca l led here i n d i s c e r n i b i l l t y r e l a t i o n . Equivalence c l a s s e s of R are ca l l ed elementary s e t s in A. Every union of elementary s e t s in A and an empty set are ca l l ed composed s e t s in A. I f X c U , then the l e a s t composed set in A containing X w i l l be ca l led the best upper approximation of X in A, and w i l l be denoted by AX. The g rea te s t composed set in A contained in A w i l l be ca l l ed the best lower approximation of X in A, and w i l l be denoted by AX. A d e f i n i t i o n of these two notions that we gave in [2] i s based on a system of axioms f o r approximations and i s d i f f e r e n t that given in [1]. In [1] and [3] [4] Z. Pawlak introduced a l so the notions of rough equa l i ty , rough inc lus ion , rough r e l a t i o n and the notion of the approximation of funct ion in the space A. Basic idea of a l l these notions i s connected with the f a c t that in some app l i ca t ions we are unable to say f o r sure whether some element belongs to the set X or not . Theory of approximations in a sense of the papers [ l ] [4 ] i s a mathematical method f o r approximate c l a s s i f i c a t i o n of o b j e c t s . In many branches of computer science these problems are of primary concern. This theory can be viewed as an a l t e r native to the theory of fuzzy s e t s [ 5 ] , and theory of to le rance space [6] , however there are some e s s e n t i a l d i f f e r e n c e s between these three theor ie s .
448 citations
TL;DR: In this paper, the authors investigated the large time behavior of the solutions of MHD equations for a viscous incompressible resistive fluid and established the regularity properties and bounds on the solutions to the equations which are valid for all time.
416 citations
TL;DR: In this article, the authors investigate the classical and semiclassical instabilities of de Sitter space and find no analog to the classical instability due to gravitational clumping of thermally excited gravitons.
287 citations
TL;DR: In this paper, the authors present a survey of the properties of multipliers in the spaces of Sobolev spaces and Bessel potentials and show that multipliers can be used to obtain a measure of functions from the spaces.
Abstract: CONTENTS Introduction Chapter I. Embedding theorems for Sobolev spaces § 1.1. The summability with respect to a measure of functions from the spaces and , § 1.2. The summability with respect to a measure of functions from the spaces and Chapter II. Multipliers in pairs of Sobolev spaces § 2.1. A description of the spaces and § 2.2. The space § 2.3. The space Chapter III. A survey of other results about spaces of multipliers § 3.1. Multipliers in pairs of spaces of Bessel potentials § 3.2. Multipliers in pairs of Slobodetskii spaces § 3.3. Some properties of multipliers § 3.4. Multipliers in pairs of Sobolev spaces in a domain § 3.5. Multipliers on the space BMO § 3.6. Multipliers on certain spaces of analytic functions § 3.7. Applications of multipliers References
242 citations
CERN1
TL;DR: In this paper, a general theory for the construction of oscillator-like unitary irreducible representations (UIRs) of non-compact supergroups in a super Fock space is given.
Abstract: We give a general theory for the construction of oscillator-like unitary irreducible representations (UIRs) of non-compact supergroups in a super Fock space. This construction applies to all non-compact supergroupsG whose coset spaceG/K with respect to their maximal compact subsupergroupK is “Hermitean supersymmetric”. We illustrate our method with the example of SU(m, p/n+q) by giving its oscillator-like UIRs in a “particle state” basis as well as “supercoherent state basis”. The same class of UIRs can also be realized over the “super Hilbert spaces” of holomorphic functions of aZ variable labelling the coherent states.
217 citations
212 citations
TL;DR: In this paper, the existence of competitive equilibrium for an economy with an infinite dimensional space of commodities was proved for an infinite-dimensional space of goods and services, and a new proof for competitive equilibrium was presented.
131 citations
TL;DR: In this paper, the authors investigated both the existence and the limiting behavior for the equation utt + Aut + Au = ƒ(t, u, ut), where A is a sectorial operator, ǫ satisfies certain regularity and growth assumptions.
126 citations
TL;DR: In this paper, the trace operator is studied in the context of modulation spaces, where B q(Rn ) and F q(rn) are modality spaces, respectively.
Abstract: respectively. Here 0 < p, q c (with p < oo in the case of the spaces F q (lt•n)). I' and F stand for the Fourier transform and its inverse, respectively, on the Schwartz space S(R). For our purpose it is sufficient to assume that / belongs to S(R) with supp F1 compact. By a suggestion of H. G. Feichtinger we denote B q(Rn ) and Fq(Rn) as modulation spaces. The main aim of this paper is to study the trace problem: What can be said about the trace operator .R,
TL;DR: The explicit construction of a dense subspace Φ of square integrable functions on the positive half of the real line is given in this paper, which has the properties that it is endowed with a metrizable nuclear topology, it is stable under multiplication by x, and the functions in Φ have suitable analytical continuation to a half plane.
Abstract: The explicit construction of a dense subspace Φ of square integrable functions on the positive half of the real line is given. This space Φ has the properties that: (1) it is endowed with a metrizable nuclear topology, (2) it is stable under multiplication by x, and (3) the functions in Φ have suitable analytical continuation to a half plane. The space Φ* of functions which are conjugate to elements of Φ is also considered. Then the triplets Φ⊆ L2 (0,∞)⊆Φ′ and Φ*⊆ L2 (0,∞)⊆Φ*′ are used to give a description of resonances.
TL;DR: In this paper, necessary and sufficient conditions for the classical Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space were established.
Abstract: We treat necessary and sufficient conditions for the classical solvability of the Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space. Our methods simultaneously embrace more general equations of Monge-Ampere type and we establish conditions which ensure that solutions have globally bounded second derivatives.
01 Jan 1983
TL;DR: In this article, the authors considered the problem of packing and covering of convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space.
Abstract: Let J be a system of sets. If all members of J are contained in a given set C and each point of C belongs to at most one member of J then J is said to be a packing into C. If, on the other hand, each point of C belongs to at least one member of J then we say that J is a covering of C. Packings and coverings have been considered in various spaces and on various combinatorial structures. Here we are interested in problems concerning packings and coverings consisting of convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space. Instead of saying that J is a packing into the whole space or J is a covering of the whole space we shall simply use the terms J is a packing and J is a covering.
TL;DR: In this paper, the authors propose a topological structure for information, where information is considered an arbitrary sub-σ-field of the σ-field (of measurable subsets of states of the world) which represents events.
TL;DR: In this paper, a particle-production mechanism for scalar lambdacphi/sup 4/ theory in de Sitter space is examined, where the rate of particle production is proportional to the number of particles present, yielding an exponentially increasing rate of production.
Abstract: We examine a particle-production mechanism for scalar lambdacphi/sup 4/ theory in de Sitter space which has the feature that the rate of particle production is proportional to the number of particles present, yielding an exponentially increasing rate of production. General arguments strongly suggest that this process is generic to any renormalizable interacting theory on de Sitter space. The interpretation of this process and its relation to the response of freely falling ''particle detectors'' is discussed.
TL;DR: In this article, the authors considered general second-order parabolic and hyperbolic equations on a bounded domain, where the feedback acts on the Dirichlet trace of the solution, and the resulting closed loop system defines a (feedback) C0-semigroup on L 2 (Ω).
TL;DR: In this article, the authors considered urban open spaces as amenity resources or local public goods and incorporated them into neoclassical urban land-use theory to determine an efficient distribution of open space.
Abstract: Urban open spaces such as parks, open squares, parkways, etc, are considered as amenity resources or local public goods and incorporated into neoclassical urban land-use theory. Models characterizing Pareto efficient allocations and competitive equilibrium allocations with open space are presented. The ‘fiscal profitability principle’ suggested by Margolis is confirmed to be applicable to determine an efficient distribution of open space. Many interesting results are established. For example, if utility function is Cobb-Douglas or log-linear, then rich will locate farther away from poor, irrespective of the distribution of open space; the optimal density distribution of open space is uniform if the spillover effects of open space are neglected, and it is decreasing with the distance from the CBD when the spillover effects of open space are taken into account.
TL;DR: Light cone cuts of null infinity as mentioned in this paper are defined to be the intersection of the light cone of an interior point xa with the future null boundary of the space-time, i.e., I+.
Abstract: Light‐cone cuts of null infinity are defined to be the intersection of the light cone of an interior point xa with the future null boundary of the space‐time, i.e., I+. It is shown how from the knowledge of the set of light‐cone cuts of I+, the interior (conformal) metric can be reconstructed. Furthermore, a differential equation defined only on I+ is proposed so that (1) the solution space (the parameters defining the set of solutions) is identified with or defines the space‐time itself and (2) the solutions themselves yield the light‐cone cuts which in turn give metrics conformally equivalent to vacuum solutions of the Einstein equations.
TL;DR: In this paper, classification of trivectors of an eight-dimensional real vector space Linear and Multilinear Algebra (LMA) is presented, with a trivector trivector of an 8-dimensional vector space.
Abstract: (1983) Classification of trivectors of an eight-dimensional real vector space Linear and Multilinear Algebra: Vol 13, No 1, pp 3-39
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TL;DR: Torretti as mentioned in this paper presents Relativity and Geometry: Relativity, Geometry, and Geometrical Geometry. Pergamon: 1983. £22.50, $45.395.
Abstract: Relativity and Geometry.By Roberto Torretti. Pergamon: 1983. Pp.395. £22.50, $45.