Search results for "analytic function"
showing 10 items of 52 documents
Nonradial Hormander algebras of several variables and convolution operators
2001
A characterization of the closed principal ideals in nonradial Hormander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quasianalytic functions, an ultradistribution on a space of quasianalytic functions is constructed such that the range of the operator does not contain the real analytic functions. Let u, v : R → R be continuous, non-negative and even functions which are increasing on the positive real numbers. We assume …
Lipschitz classes and the Hardy-Littlewood property
1993
We study the geometry of plane domains and the uniform Holder continuity properties of analytic functions.
Frames and representing systems in Fréchet spaces and their duals
2014
[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.
Some spectral mapping theorems through local spectral theory
2004
The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a re…
Some algebras of symmetric analytic functions and their spectra
2011
AbstractIn the spectrum of the algebra of symmetric analytic functions of bounded type on ℓp, 1 ≤ p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on ℓ1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of ℓ1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.
WEAKLY COMPACT HOMOMORPHISMS BETWEEN SMALL ALGEBRAS OF ANALYTIC FUNCTIONS
2001
The weak compactness of the composition operator CΦ(f) = f ○ Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.
Planar Mappings of Finite Distortion
2010
We review recent results on planar mappings of finite distortion. This class of mappings contains all analytic functions and quasiconformal mappings.
Interpolating sequences for bounded analytic functions
2007
. We prove that any sequence in the open ball of a complex Banach space E, even in that of E**, whose norms are an interpolating sequence for H∞, is interpolating for the space of all bounded analytic functions on BE-The construction made yields that the interpolating functions depend linearly on the interpolated values.
Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient
2008
We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ preserves sets with vanishing analytic capacity. It then follows that a compact set $E$ is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in $W^{1,2}$.
Fractional viscoelastic beam under torsion
2017
Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.