The Hadamard Product as a Universality Preserving Operator

Müller, Jürgen; Pohlen, T.

doi:10.1007/bf03321768

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The Extended Hadamard Product1

Introduction1

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2022

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Cited by 5 publications

(3 citation statements)

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“…This new definition led to interesting applications, (e.g. [8] and [10]). In this introduction, we shall recall the construction and the results of T. Pohlen.…”

Section: The Extended Hadamard Productmentioning

confidence: 99%

Holomorphic cohomological convolution and Hadamard product

Dubussy¹,

Schneiders²

2018

Preprint

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“…This new definition led to interesting applications, (e.g. [8] and [10]). In this introduction, we shall recall the construction and the results of T. Pohlen.…”

Section: The Extended Hadamard Productmentioning

confidence: 99%

Holomorphic cohomological convolution and Hadamard product

Dubussy¹,

Schneiders²

2018

Preprint

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“…It was extensively studied in various aspects: as a bilinear form, as a linear operator with one factor fixed (see the survey [19] and, for instance, the papers [1], [2], [3], [4], [12], [14], [15], [16], [17], [18], [20], [21], [22], [25]), and also as a map acting on spaces of real analytic functions (see [6], [7], [8], [9], [10], [11]).…”

Section: Introductionmentioning

confidence: 99%

The $*$-product of domains in several complex variables

Zajac¹

2021

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In this article we continue the research, carried out in [25], on computing the * -product of domains in C N . Assuming that 0 ∈ G ⊂ C N is an arbitrary Runge domain and 0 ∈ D ⊂ C N is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between D * G and another domain in C N which is 'extremal' (in an appropriate sense) with respect to a special coefficient multiplier dependent only on the dimension N . Next, for N = 2, we derive a characterization of the latter domain expressed in terms of planar geometry. These two results, when combined together, give a formula which allows to calculate D * G for two-dimensional domains D and G satisfying the outlined assumptions.

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“…This new definition led to interesting applications (e.g. [12] and [15]). In this introduction, we shall recall the construction and the results of Pohlen.…”

mentioning

confidence: 99%