In this paper, inspired by the work of Lawson and Xu, we consider the question of what classes A of topological spaces should be paired with classes B of domains in order that the Isbell and Scott topologies on functi...
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In this paper, inspired by the work of Lawson and Xu, we consider the question of what classes A of topological spaces should be paired with classes B of domains in order that the Isbell and Scott topologies on function spaces [A -> B] are identical for A is an element of A and B is an element of B. It is shown that: (1) if A and B are restricted to be a class of core compact spaces and a class of bicomplete domains respectively, a class of core compact and compact spaces is paired with a class of conditionally bounded complete domains;(2) if A and B are restricted to be a class of core compact and locally connected spaces and a class of bicomplete domains respectively, a class of topological spaces called RW-spaces (with finitely many connected components), which was first introduced by Kou and Luo and further studied by Lawson and Xu later, is paired with a class of pointed L-domains (disjoint union of pointed L-domains). This also gives a solution to a problem posed by Kou and Luo. (C) 2017 Elsevier B.V. All rights reserved.
A set A subset of C-p(X) is uniformly dense in C-p(X) if, for any f is an element of C-p(X) and epsilon > 0, there is g is an element of A such that vertical bar g(x) - f (x)vertical bar < epsilon for all x is a...
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A set A subset of C-p(X) is uniformly dense in C-p(X) if, for any f is an element of C-p(X) and epsilon > 0, there is g is an element of A such that vertical bar g(x) - f (x)vertical bar < epsilon for all x is an element of X. We prove that C-p(X) has a uniformly dense subspace that condenses onto a second countable space if and only if C-p (X) has cardinality of the continuum. This answers a question of Tkachuk published in 2003. It is also proved that C-p(X) has a dense F-sigma-metrizable subspace if X is metrizable or Eberlein compact. If X is Corson compact or C-p(X) is a Lindelof Sigma-space, then it is possible to find a dense set Y subset of C-p(X) with countable pseudocharacter. (C) 2017 Elsevier B.V. All rights reserved.
We demonstrate that any surjective isometry T : A -> B not assumed to be linear between unital, completely regular subspaces of complex valued, continuous functions on compact Hausdorff spaces is of the form T(f) =...
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We demonstrate that any surjective isometry T : A -> B not assumed to be linear between unital, completely regular subspaces of complex valued, continuous functions on compact Hausdorff spaces is of the form T(f) = T(0) _ Re [mu.(fo tau)] + ilm[nu.(fo rho)], where mu and nu are continuous and unimodular, there exists a clopen set K with nu-mu on K and nu - -mu on K degrees , and tau and rho are homeomorphisms.
In this paper we describe, under certain assumptions, surjective diameter preserving mappings when defined between function spaces, not necessarily algebras, thus extending most of the previous results for these opera...
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In this paper we describe, under certain assumptions, surjective diameter preserving mappings when defined between function spaces, not necessarily algebras, thus extending most of the previous results for these operators. We provide an example which shows that our assumptions are not redundant.
We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by consi...
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We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters s, n, and Q, we establish connections between the variational formulations of these theories. We use these results to justify a version of the Oseen-Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director.
Let theta is an element of R, 1 0)[t(theta)parallel to U(t)(f)parallel to(p)] <+ infinity and their relation with the standard Besov spaces. We also prove some results related to the Schrodinger equation. (C) 2015 ...
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Let theta is an element of R, 1 <= p < + infinity and consider the Schrodinger group U(t) = e(it Delta) In this study, our main goal is to investigate the space E-p(theta) of distributions f on R-n that satisfy sup(t>0)[t(theta)parallel to U(t)(f)parallel to(p)] <+ infinity and their relation with the standard Besov spaces. We also prove some results related to the Schrodinger equation. (C) 2015 Published by Elsevier Inc.
The fractional Fourier transform (FRET) has proven to be a powerful tool in optics and signal processing. Sampling theory of this transform for band-limited signals has blossomed in recent years. However, real-world s...
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The fractional Fourier transform (FRET) has proven to be a powerful tool in optics and signal processing. Sampling theory of this transform for band-limited signals has blossomed in recent years. However, real-world signals are often not band-limited. In this paper, we first develop the theory of frames for function spaces associated with the FRFT, then we propose a general framework for FRFT-based sampling and reconstruction in function spaces without band-limiting constraints. Based upon the proposed framework, a simple necessary and sufficient condition for FRFT-based uniform sampling in function spaces is found, which facilitates a straightforward derivation of the uniform sampling theorem for the FRFT. The theoretical derivations are validated by the means of numerical results. (C) 2014 Elsevier B.V. All rights reserved.
The paper deals with solutions of nonlinear heat and Navier-Stokes equations in the context of Besov and Triebel-Lizorkin spaces and where 1 <= p, q <= infinity and -1 + n/p < s < n/p.
The paper deals with solutions of nonlinear heat and Navier-Stokes equations in the context of Besov and Triebel-Lizorkin spaces and where 1 <= p, q <= infinity and -1 + n/p < s < n/p.
We investigate certain recently introduced ODE-determined varying exponent L-P spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent l(P) space. Moreover, this can ...
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We investigate certain recently introduced ODE-determined varying exponent L-P spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent l(P) space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above L-P spaces to an ultrapower of the above varying exponent l(P) space.
We study systematically when C-p(X) has a topological property P if C-p(X) is discretely P. i.e., the set (D) over bar has P for every discrete subspace D subset of C-p(X). We prove that it is independent of ZFC wheth...
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We study systematically when C-p(X) has a topological property P if C-p(X) is discretely P. i.e., the set (D) over bar has P for every discrete subspace D subset of C-p(X). We prove that it is independent of ZFC whether discrete metrizability of C-p(X) implies its metrizability for a compact space X. We show that it is consistent with ZFC that countable tightness and Lindelof Sigma-property are not discretely reflexive in spaces C-p(X). It is also established that a space X must be countable and discrete if C-p(X) is discretely Cech-complete. If C-p(X) is discretely sigma-compact then X has to be finite.
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