Search results for "bound"
showing 10 items of 2948 documents
Existence theorems for inclusions of the type
1999
For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chiefly using Ky Fan's fixed point principle. The main result of the paper improves Theorem 1 in [16] as well as Theorem 2.2 of [3]. Some meaningful concrete cases are also presented and discussed.
Refinements of PIP-Spaces
2009
We have seen in Section 1.5, that the compatibility relation underlying a pip-space may always be coarsened, but not refined in general. There is an exception, however, namely the case of a scale of Hilbert spaces and analogous structures. We shall describe it in this section.
Partial O*-Algebras
2002
This chapter is devoted to the investigation of partial O*-algebras of closable linear operators defined on a common dense domain in a Hilbert space. Section 2.1 introduces of O- and O*-families, O- and O*-vector spaces, partial O*-algebras and O*-algebras. Partial O*-algebras and strong partial O*-algebras are defined by the weak and the strong multiplication. Section 2.2 describes four canonical extensions (closure, full-closure, adjoint, biadjoint) of O*-families and defines the notions of closedness and full-closedness (self-adjointness, integrability) of O*-families in analogy with that of closed (self-adjoint) operators. Section 2.3 deals with two weak bounded commutants M′w and M′qw …
Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions
2008
AbstractWe determine the spectra of composition operators acting on weighted Banach spaces Hv∞ of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.
Tethyan vs. Cordilleran ophiolites: a reappraisal of distintctive tectono-magmatic features of supra-subduction complexes in relation to the subducti…
2004
Abstract Supra-subduction zone (SSZ) ophiolites deserve special attention because they represent fundamental markers of intraoceanic convergence and generation of new lithosphere above subduction zones. Moreover, owing to their structural characteristics and location in the overriding plate, these complexes are far better represented and preserved than Mid-Ocean-Ridge-Basalt (MORB) ophiolites in orogenic belts. In terms of their structure, tectonics, and magmatic features, SSZ ophiolites may be classified in two main types: (1) “Tethyan complexes” (such as those of the Albanide-Hellenide belt), which mostly consist of complete and extensive volcanic, dyke, plutonic, and mantle sections with…
Crystal-Plastic Deformation, Recovery and Recrystallisation of Quartz
2009
As stated in the introduction, this chapter is included because of the special importance of quartz to estimate metamorphic conditions during and after mylonitisation. The theory behind crystal-plastic deformation is treated elsewhere (e.g. Passchier & Trouw 2005). The main optical expression of crystal-plastic deformation is smooth, non-patchy undulose extinction. Elongated grains with such undulose extinction, sometimes accompanied by deformation lamellae, are indicative for low-temperature deformation. At slightly higher temperatures recovery produces subgrains and recrystallisation tends to substitute the old deformed grains by small new ones. Three types of recrystallisation can be dis…
High-Grade Mylonites
2009
High-grade mylonites are formed at temperatures above 650 °C. They are relatively uncommon, probably because their conservation is problematic. Most mylonites formed under these conditions would tend to fully recrystallise which destroys and masks the mylonitic structure. Mylonitic features are only preserved if grain growth is somehow inhibited in the rock, e.g. by its polymineralic nature.
Operator martingale decomposition and the Radon-Nikodym property in Banach spaces
2010
Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …
Quasihyperbolic boundary conditions and capacity: Uniform continuity of quasiconformal mappings
2005
We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.
Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
2014
We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.