Hadamard Multipliers on Spaces of Holomorphic Functions

Abstract

Abstract. Several representation theorems of multipliers are derived: in terms of analytic functionals, and germs of holomorphic functions. The co-induced topology via the representation theorems is discussed. As an application of the representation theorems the density of non-invertible multipliers is proved. Moreover, Euler differential operators are distinguished among all multipliers.Mathematics Subject Classification. 30H10, 46F15, 44A35, 30B40.

One-Sided Invertibility of Toeplitz Operators on the Space of Real Analytic Functions on the Real Line

“…This is precisely the equation which we obtained in (42). Therefore the same choice of f and the sequences p N n will lead to a contradiction.…”

“…These are the operators the associated matrix of which is just diagonal. This research was continued by Domański et al [15] and also by Vogt in [44,45] for spaces of distributions, in [43] for spaces of smooth functions and by Trybu la in [42] for spaces of holomorphic functions. In [14] and [16] Domański and Langenbruch showed that this theory provides the correct framework to study Euler's equation.…”

Toeplitz operators on the space of all holomorphic functions on finitely connected domains

“…We only mention the articles which have had some impact on our research. This includes the results by Albanese, Bonet and Ricker [2][3][4][5], Bonet, Lusky and Taskinen [10,11], Bonet and Domański [9], Bonet and Taskinen [12] and also Trybuła [43]. Some of this research concerns Toeplitz operators on weighted sup-norm spaces.…”

Operators of Almost Hadamard-Type and the Hardy-Littlewood Operator in the Space of Entire Functions of Several Complex Variables

“…В пространстве 𝐻(Ω) всех голоморфных функций в односвязной области Ω ⊂ C полная характеризация диагональных операторов получена Линчуком [1], Братищевым [2] (см. также [3; § 9]), Трибулой [4]. Доманский, Лангенбрух и Фогт [5]- [9] исследовали операторы адамаровского типа в пространстве вещественно аналитических функций на открытом множестве Ω ⊂ R 𝑁 .…”