DSpace Collection: Volume 36, Number 4
http://hdl.handle.net/10525/2685
Serdica Mathematical Journal Volume 36, Number 4, 2010The Collection's search engineSearch the Channelsearch
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Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
http://hdl.handle.net/10525/2711
Title: Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials<br/><br/>Authors: Jules, Florence; Lassonde, Marc<br/><br/>Abstract: We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz Separation property, a strong Compact Separation property and a Minimal property for the analytic approximate subdifferential of Ioffe.<br/><br/>Description: 2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.Fri, 01 Jan 2010 00:00:00 GMTPlus-Minus Property as a Generalization of the Daugavet Property
http://hdl.handle.net/10525/2710
Title: Plus-Minus Property as a Generalization of the Daugavet Property<br/><br/>Authors: Shepelska, Varvara<br/><br/>Abstract: It was shown in [2] that the most natural equalities valid for every rank-one operator T in real Banach spaces lead either to the Daugavet equation ||I+T|| = 1 + ||T|| or to the equation ||I − T|| = ||I+T||. We study if the spaces where the latter condition is satisfied for every finite-rank operator inherit the properties of Daugavet spaces.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42.Fri, 01 Jan 2010 00:00:00 GMTLocal Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates
http://hdl.handle.net/10525/2709
Title: Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates<br/><br/>Authors: Kian, Yavar<br/><br/>Abstract: We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to {θ ∈ C : Im(θ) ≥ 0}, for n ≥ 3, odd, and to {θ ∈ C : Im(θ) ≥ 0, θ ≠ 2kπ − iμ, k ∈ Z, μ ≥ 0} for n ≥ 4, even, and for n ≥ 4 even Rχ(θ) is bounded in a neighborhood of θ = 0.<br/><br/>Description: 2000 Mathematics Subject Classification: 35B40, 35L15.Fri, 01 Jan 2010 00:00:00 GMTSelections, Paracompactness and Compactness
http://hdl.handle.net/10525/2708
Title: Selections, Paracompactness and Compactness<br/><br/>Authors: Choban, Mitrofan M.; Mihaylova, Ekaterina P.; Nedev, Stoyan I.<br/><br/>Abstract: In the present paper the Lindelöf number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.<br/><br/>Description: 2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.Fri, 01 Jan 2010 00:00:00 GMT