Let P be a topological property. A.V. Arhangel'skii calls X projectively P if every second countable continuous image of X is P. Lj.D.R. KoCinac characterized the classical covering properties of Menger, Rothberge...
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Let P be a topological property. A.V. Arhangel'skii calls X projectively P if every second countable continuous image of X is P. Lj.D.R. KoCinac characterized the classical covering properties of Menger, Rothberger, Hurewicz and Gerlits-Nagy in term of continuous images in R-omega. In this paper we study the functional characterizations of all projective versions of the selection properties in the Scheepers Diagram. (C) 2020 Elsevier B.V. All rights reserved.
In this paper we study the selection principle of closed discrete selection, first researched by Tkachuk in [12] and strengthened by Clontz, Holshouser in [3], in set-open topologies on the space of continuous real-va...
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In this paper we study the selection principle of closed discrete selection, first researched by Tkachuk in [12] and strengthened by Clontz, Holshouser in [3], in set-open topologies on the space of continuous real-valued functions. Adapting the techniques involving point-picking games on X and C-p(X), the current authors showed similar equivalences in [ 1] involving the compact subsets of X and C-kappa(X). By pursuing a bitopological setting, we have touched upon a unifying framework which involves three basic techniques: general game duality via reflections (Clontz), general game equivalence via topological connections, and strengthening of strategies (Pawlikowski and Tkachuk). Moreover, we develop a framework which identifies topological notions to match with generalized versions of the point-open game. (C) 2020 Elsevier B.V. All rights reserved.
The linear canonical transform (LCT) has been shown to be useful and powerful in signal processing, optics, etc. Many results of this transform are already known, including sampling theory. Most existing sampling theo...
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The linear canonical transform (LCT) has been shown to be useful and powerful in signal processing, optics, etc. Many results of this transform are already known, including sampling theory. Most existing sampling theories of the LCT consider the class of bandlimited signals. However, in the real world, many analog signals arising in engineering applications are non-bandlimited. In this correspondence, we propose a sampling and reconstruction strategy for a class of function spaces associated with the LCT, which can provide a suitable and realistic model for real applications. First, we introduce definitions of semi-and fully-discrete convolutions for the LCT. Then, we derive necessary and sufficient conditions pertaining to the LCT, under which integer shifts of a chirp-modulated function generate a Riesz basis for the function spaces. By applying the results, we present a more comprehensive sampling theory for the LCT in the function spaces, and further, a sampling theorem which recovers a signal from its own samples in the function spaces is established. Moreover, some sampling theorems for shift-invariant spaces and some existing sampling theories for bandlimited signals associated with the Fourier transform (FT), the fractional FT, or the LCT are noted as special cases of the derived results. Finally, some potential applications of the derived theory are presented.
In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along wi...
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In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to elliptic boundary value problems.
We study Kadec-Klee properties with respect to global (local) convergence in measure. First, we present some results concerning Kothe spaces and Orlicz functions. Next, we shall give full criteria for Kadec-Klee prope...
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We study Kadec-Klee properties with respect to global (local) convergence in measure. First, we present some results concerning Kothe spaces and Orlicz functions. Next, we shall give full criteria for Kadec-Klee properties with respect to global (local) convergence in measure in Calderon-Lozanovskii function spaces. In particular, we obtain the full characterizations of Kadec-Klee properties in Orlicz-Lorentz function spaces, which have not been presented until now.
Let (X, tau) be a topological space and let rho be a metric defined on X. We shall say that (X, tau) is fragmented by p if whenever epsilon > 0 and A is a nonempty subset of X there is a tau-open set U such that U ...
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Let (X, tau) be a topological space and let rho be a metric defined on X. We shall say that (X, tau) is fragmented by p if whenever epsilon > 0 and A is a nonempty subset of X there is a tau-open set U such that U boolean AND A not equal empty set and rho - diam(U boolean AND A) < epsilon. In this paper we consider the notion of fragmentability, and its generalisation sigma-fragmentability, in the setting of topological groups and metric-valued function spaces. We show that in the presence of Baireness fragmentability of a topological group is very close to metrizability of that group. We also show that for a compact Hausdorff space X, sigma-fragmentability of (C(X). parallel to . parallel to(infinity)) implies that the space C(p)(X: M) of all continuous functions from X into a metric space M. endowed with the topology of pointwise convergence on X, is fragmented by a metric whose topology is at least as strong as the uniform topology on C(X: M). The primary tool used is that of topological games. (C) 2011 Elsevier B.V. All rights reserved.
We characterize complex measures mu on the unit ball of C-n, for which the general Toeplitz operator T-mu(alpha) is bounded or compact on the analytic Besov spaces B-p(B-n), also on the minimal Mobius invariant Banach...
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We characterize complex measures mu on the unit ball of C-n, for which the general Toeplitz operator T-mu(alpha) is bounded or compact on the analytic Besov spaces B-p(B-n), also on the minimal Mobius invariant Banach spaces B-1(B-n) in the unit ball B-n.
We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(rho) = C (gamma) rho (gamma) for gamma > 1. The physical vac...
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We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(rho) = C (gamma) rho (gamma) for gamma > 1. The physical vacuum singularity requires the sound speed c to go to zero as the square-root of the distance to the moving boundary, and thus creates a degenerate and characteristic hyperbolic free-boundary system wherein the density vanishes on the free-boundary, the uniform Kreiss-Lopatinskii condition is violated, and manifest derivative loss ensues. Nevertheless, we are able to establish the existence of unique solutions to this system on a short time-interval, which are smooth (in Sobolev spaces) all the way to the moving boundary, and our estimates have no derivative loss with respect to initial data. Our proof is founded on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term, chosen to preserve as much of the geometric structure of the Euler equations as possible. We first construct solutions to this degenerate parabolic regularization using a higher-order version of Hardy's inequality;we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter. Solutions to the compressible Euler equations are found in the limit as the artificial viscosity tends to zero. Our regular solutions can be viewed as degenerate viscosity solutions. Our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws.
Differential operators generated by homogeneous functions psi of an arbitrary real order s > 0 (psi-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically st...
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Differential operators generated by homogeneous functions psi of an arbitrary real order s > 0 (psi-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for psi-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.
We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levi in 2009. The study of these function spaces was initiated...
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We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levi in 2009. The study of these function spaces was initiated in [G. Beer, S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350 (2009) 568-589] and A. Caserta, G. Di Maio, L'. Hola, Arzela's Theorem and strong uniform convergence on bornologies, J. Math. Anal. Appl. 371 (2010) 384-392]. The properties we study are related to selection principles. (c) 2011 Elsevier B.V. All rights reserved.
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