Search results for "Analytic function"
showing 10 items of 52 documents
Certain subclasses of multivalent analytic functions defined by multiplier transforms
2010
By making use of the principle of subordination between analytic functions and a family of multiplier transforms, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships, subordination and superordination properties, integral-preserving properties, argument estimates and convolution properties are proved.
The convolution operation on the spectra of algebras of symmetric analytic functions
2012
Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.
Gleason Parts and Weakly Compact Homomorphismsbetween Uniform Banach Algebras
1999
If points in nontrivial Gleason parts of a uniform Banach algebra have unique representing measures, then the weak and the norm topology coincide on the spectrum. We derive from this several consequences about weakly compact homomorphisms and discuss the case of other uniform Banach algebras arising in complex infinite dimensional analysis.
Modulus of continuity with respect to semigroups of analytic functions and applications
2016
Abstract Given a complex Banach space E , a semigroup of analytic functions ( φ t ) and an analytic function F : D → E we introduce the modulus w φ ( F , t ) = sup | z | 1 ‖ F ( φ t ( z ) ) − F ( z ) ‖ . We show that if 0 α ≤ 1 and F belongs to the vector-valued disc algebra A ( D , E ) , the Lipschitz condition M ∞ ( F ′ , r ) = O ( ( 1 − r ) 1 − α ) as r → 1 is equivalent to w φ ( F , t ) = O ( t α ) as t → 0 for any semigroup of analytic functions ( φ t ) , with φ t ( 0 ) = 0 and infinitesimal generator G , satisfying that φ t ′ and G belong to H ∞ ( D ) with sup 0 ≤ t ≤ 1 ‖ φ ′ ‖ ∞ ∞ , and in particular is equivalent to the condition ‖ F − F r ‖ A ( D , E ) = O ( ( 1 − r ) α ) as r …
Cluster values of holomorphic functions of bounded type
2015
We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. Fil: Aron, Richard Martin. Kent State University; Estados Unidos Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Lassalle, S…
Interpolating sequences on uniform algebras
2009
Abstract We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c 0 , then it is sufficient for any dual uniform algebra.
Embedding of analytic function spaces with given mean growth of the derivative
2006
MSC (2000) 30D55 If φ is a positive function defined in (0,1) and 0 <p< ∞, we consider the space L(p, φ) which consists of all functions f analytic in the unit disc D for which the integral means of the derivative Mp(r, f � )= " 1 2π Rπ −π þ f � (re iθ ) þ p dθ "1/p , 0 <r< 1, satisfy M p(r, f � )=O (φ(r)) ,a sr → 1. In this paper, for any given p ∈ (0,1), we characterize the functions φ, among a certain class of weight functions, to be able to embedd L(p, φ) into classical function spaces. These results complement other previously obtained by the authors for p ≥ 1. c
The Line Element-less Method Analysis of orthotropic beam for the De Saint Venant torsion problem
2010
Abstract This paper deals with the extension of a novel numerical technique, labelled line element-less method (LEM), in order to provide approximate solutions of the De Saint Venant torsion problem for orthotropic beams having simply and multiply connected cross-section. A suitable transformation of coordinates allows to take full advantage of the theory of analytic complex functions as in the isotropic case. A complex potential function analytic in all the transformed domain whose real and imaginary parts are related to the shear stress components and to the orthotropic ratio is introduced and expanded in the double-ended Laurent series involving harmonic polynomials. An element-free weak…
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method
2021
Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…