Dynamics of the Volterra-Type Integral and Differentiation Operators on Generalized Fock Spaces

Bonet, José; Mengestie, Tesfa; Worku, Mafuz

doi:10.1007/s00025-019-1123-7

Cited by 3 publications

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References 29 publications

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“…Extensions of these results for more general weighted Banach spaces of entire functions were obtained by Beltrán [27], Bonilla and the author [46] and Mengestie, Worku and the author in [64]. The case of differentiation and integration operators acting on Hörmander algebras was studied in [31].…”

Section: Proposition 35 the Operator J Is Never Hypercyclic On H 0 V ...mentioning

confidence: 99%

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Bonet

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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In this survey we report about recent work on weighted Banach spaces of analytic functions on the unit disc and on the whole complex plane defined with sup-norms and operators between them. Results about the solid hull and core of these spaces and distance formulas are reviewed. Differentiation and integration operators, Cesàro and Volterra operators, weighted composition and superposition operators and Toeplitz operators on these spaces are analyzed. Boundedness, compactness, the spectrum, hypercyclicity and (uniform) mean ergodicity of these operators are considered.

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Section: Proposition 35 the Operator J Is Never Hypercyclic On H 0 V ...mentioning

confidence: 99%

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Bonet

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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“…Thus, the novelty to enrich D with some basic structures is the fact that it acts between two different underlying spaces, that is, β ̸ = α. In contrast, following the description in Theorem 1.1, several dynamical properties of D have been recently studied on the spaces F p ψm [6]. When α = β = 1, the spaces F p α correspond to the classical Fock spaces, and Theorem 1.2 reiterates that the operator D has no bounded structure in its action on them.…”

Section: Introductionmentioning

confidence: 99%

On the differential and Volterra-type integral operators on Fock-type spaces

Mengestie¹

2022

Revista De La Unión Matemática Argentina

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The differential operator fails to admit some basic structures including continuity when it acts on the classical Fock spaces or weighted Fock spaces, where the weight functions grow faster than the classical Gaussian weight function. The same conclusion also holds in some weighted Fock spaces including the Fock-Sobolev spaces, where the weight functions grow more slowly than the Gaussian function. We consider modulating the classical weight function and identify Fock-type spaces where the operator admits the basic structures. We also describe some properties of Volterra-type integral operators on these spaces using the notions of order and type of entire functions. The modulation operation supplies richer structures for both the differential and integral operators in contrast to the classical setting.

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Surjective and closed range differentiation operator

Mengestie

2024

Rend. Circ. Mat. Palermo, II. Ser

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We identify Fock-type spaces $$\mathcal {F}_{(m,p)}$$ F ( m , p ) on which the differentiation operator D has closed range. We prove that D has closed range only if it is surjective, and this happens if and only if $$m=1$$ m = 1 . Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition–differentiation operator, $$D_{(u,\psi ,n)} f= u\cdot \big ( f^{(n)}\circ \psi \big )$$ D ( u , ψ , n ) f = u · ( f ( n ) ∘ ψ ) , on these spaces and describe conditions under which the operator admits closed range, surjective, and order bounded structures.

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Dynamics of the Volterra-Type Integral and Differentiation Operators on Generalized Fock Spaces

Cited by 3 publications

References 29 publications

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

On the differential and Volterra-type integral operators on Fock-type spaces

Surjective and closed range differentiation operator

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