We obtain improved versions of a classical theorem of Rogosinski concerning the partial sums of a bounded holomorphic function defined on the open unit disk D. Further, we establish refined versions ...of a generalized Bohr inequality for holomorphic functions mapping D inside a simply connected or convex domain Ω⊊C. In addition, we improve on the classical Bohr inequality for the family of holomorphic self mappings of D and for its subfamily consisting of functions that fix the origin.
We give descriptions for algebra homomorphisms and automorphisms of vector-valued bounded holomorphic functions defined on the open unit disc. The characterizations derived allow us to establish the ...algebraic reflexivity properties of the group of automorphisms on these spaces.
In this paper, we first establish a version of multidimensional analogues of the refined Bohr's inequality. Then we establish two versions of multidimensional analogues of improved Bohr's inequality ...with initial coefficient being zero. Finally we establish two versions of multidimensional analogues of improved Bohr's inequality with the initial coefficient being replaced by absolute value of the function, and to prove that most of the results are sharp.
We give a capacitary type characterization of Carleson measures for a class of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel upper half-space, introduced by Arcozzi et ...al. in 7. This answers in part a question raised by the same authors.
Linear isometries of Hol(D) Chalendar, I.; Oger, L.; Partington, J.R.
Journal of mathematical analysis and applications,
12/2024, Letnik:
540, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out ...to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. Finally, the spectra of such operators are studied.
In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit ...disk U, which are associated with the Bazilevič functions and the λ-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family SWΣ(δ,γ,λ,s,t,q,r). Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function Φ(z,s,a) is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself.
Let φ:D→D be a holomorphic map with a fixed point α∈D such that 0≤|φ′(α)|<1. We show that the spectrum of the composition operator Cφ on the Fréchet space Hol(D) is {0}∪{φ′(α)n:n=0,1,⋯} and its ...essential spectrum is reduced to {0}. This contrasts the situation where a restriction of Cφ to Banach spaces such as H2(D) is considered. Our proofs are based on explicit formulae for the spectral projections associated with the point spectrum found by Koenigs. Finally, as a byproduct, we obtain information on the spectrum for bounded composition operators induced by a Schröder symbol on arbitrary Banach spaces of holomorphic functions.
Finite type points on subsets of Cn Yazici, Ozcan
Journal of mathematical analysis and applications,
07/2020, Letnik:
487, Številka:
1
Journal Article
Recenzirano
In 4, D'Angelo introduced the notion of points of finite type for a real hypersurface M⊂Cn and showed that the set of points of finite type in M is open. Later, Lamel-Mir 8 considered a natural ...extension of D'Angelo's definition for an arbitrary set M⊂Cn. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M⊂Cn.
Let φ={φk}k=−∞∞ denote the extended Takenaka–Malmquist system on unit circle T and let σn,φ(f), f∈L1(T), be the Fejér-type operator based on φ, introduced by V. N. Rusak. We give the convergence ...criteria for σn,φ(f) in Banach space C(T). Also we prove the Voronovskaya-type theorem for σn,φ(f) on class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
We show that the duals of Banach algebras of scalar-valued bounded holomorphic functions on the open unit ball BE of a Banach space E lack weak⁎-strongly exposed points. Consequently, we obtain that ...some Banach algebras of holomorphic functions on an arbitrary Banach space have the Daugavet property which extends the observation of P. Wojtaszczyk 56. Moreover, we present a new denseness result by proving that the set of norm-attaining vector-valued holomorphic functions on the open unit ball of a dual Banach space is dense provided that its predual space has the metric π-property. Besides, we obtain several equivalent statements for the Banach space of vector-valued homogeneous polynomials to be reflexive, which improves the result of J. Mujica 47, J. A. Jaramillo and L. A. Moraes 39. As a byproduct, we generalize some results on polynomial reflexivity due to J. Farmer 35.
PDF
