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...
详细信息
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.
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...
详细信息
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.
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 ...
详细信息
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...
详细信息
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...
详细信息
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...
详细信息
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...
详细信息
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.
In this paper, we consider the performance of sampling associated with the linear canonical transform (LCT), which generalizes a large number of classical integral transforms and fundamental operations linked to signa...
详细信息
In this paper, we consider the performance of sampling associated with the linear canonical transform (LCT), which generalizes a large number of classical integral transforms and fundamental operations linked to signal processing and optics. First, we revisit sampling approximation in the LCT domain to introduce a generalized approximation operator. Then, we derive an exact closed-form expression for the integrated squared error that occurs when a signal is approximated by a basis of shifted, scaled, and chirp-modulated versions of a generating function in the LCT domain. Several basic properties of the approximation error are presented. The derived results can be applied to a wide variety of sampling approximation schemes in the LCT domain. Finally, experimental examples are given to illustrate the theoretical derivations.
We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation u(t)=U(t,s)u(s)+(s)integral U-t(t,xi)f(xi,u(xi))d xi in the case where the evolution fami...
详细信息
We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation u(t)=U(t,s)u(s)+(s)integral U-t(t,xi)f(xi,u(xi))d xi in the case where the evolution family (U(t, s))(t >= s) has an exponential trichotomy on a half line or on the whole line, and the nonlinear forcing term f satisfies the phi-Lipschitz conditions, i.e., parallel to f(t, x) - f(t, y)parallel to <=phi(t)parallel to x - y parallel to, where phi(t) belongs to some classes of admissible function spaces. Our main method is based on the Lyapunov-Perron methods, rescaling procedures, and the techniques of using the admissibility of function spaces.
We give a decomposition for the dual space of some Banach function spaces as the Zygmund space EXP alpha of the exponential integrable functions, the Marcinkiewicz space L-p,L-infinity, and the Grand Lebesgue Space L-...
详细信息
We give a decomposition for the dual space of some Banach function spaces as the Zygmund space EXP alpha of the exponential integrable functions, the Marcinkiewicz space L-p,L-infinity, and the Grand Lebesgue Space L-p),L-theta.
暂无评论