Search results for "mathematical analysis"

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.

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.

Menger curvature and Lipschitz parametrizations in metric spaces

2005

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)∣.

Resonant neumann equations with indefinite linear part

2015

We consider aseminonlinear Neumann problem driven by the $p$-Laplacian plus an indefinite and unbounded potential. The reaction of the problem is resonant at $\pm \infty$ with respect to the higher parts of the spectrum. Using critical point theory, truncation and perturbation techniques, Morse theory and the reduction method, we prove two multiplicity theorems. One produces three nontrivial smooth solutions and the second four nontrivial smooth solutions.

Bloch functions on the unit ball of an infinite dimensional Hilbert space

2015

The Bloch space has been studied on the open unit disk of C and some ho- mogeneous domains of C n . We dene Bloch functions on the open unit ball of a Hilbert space E and prove that the corresponding space B(BE) is invariant under composition with the automorphisms of the ball, leading to a norm that- modulo the constant functions - is automorphism invariant as well. All bounded analytic functions on BE are also Bloch functions. ones, resulting the fact that if for a given n; the restrictions of the function to the n-dimensional subspaces have their Bloch norms uniformly bounded, then the function is a Bloch one and conversely. We also introduce an equivalent norm forB(BE) obtained by repla…

Homeomorphisms of finite distortion: discrete length of radial images

2008

AbstractWe study homeomorphisms of finite exponentially integrable distortion of the unit ball Bn onto a domain Ω of finite volume. We show that under such a mapping the images of almost all radii (in terms of a gauge dimension) have finite discrete length. We also show that our dimension estimate is essentially sharp.

Conformal Metrics on the Unit Ball in Euclidean Space

1998