2016
DOI: 10.1016/j.jat.2015.02.006
|View full text |Cite
|
Sign up to set email alerts
|

Density of certain polynomial modules

Abstract: In this paper the problem of density in the space C(X ), for a compact set X ⊂ C, of polynomial modules of the type { p + z d q: p, q ∈ C[z]} for integer d > 1, as well as several related problems are studied. We obtain approximability criteria for Carathéodory compact sets using the concept of a d-Nevanlinna domain, which is a new special analytic characteristic of planar simply connected domains. In connection with this concept we study the problem of taking roots in the model spaces, that is, in the subspac… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
8
0
1

Year Published

2016
2016
2023
2023

Publication Types

Select...
5
1
1

Relationship

0
7

Authors

Journals

citations
Cited by 12 publications
(9 citation statements)
references
References 19 publications
0
8
0
1
Order By: Relevance
“…Later on, several interesting and important results about uniform approximation by polyanalytic polynomials were obtained in [15,10,6,8,1]. The keynote ingredient of these results is the concept of a Nevanlinna domain and several its special refinements and modifications.…”
Section: Background Information On the Nevanlinna Domainsmentioning
confidence: 99%
See 2 more Smart Citations
“…Later on, several interesting and important results about uniform approximation by polyanalytic polynomials were obtained in [15,10,6,8,1]. The keynote ingredient of these results is the concept of a Nevanlinna domain and several its special refinements and modifications.…”
Section: Background Information On the Nevanlinna Domainsmentioning
confidence: 99%
“…We use the construction of an H-tree described in the proof of Theorem 3 and some other notations from that proof. We suppose that dim H (H ∞ ) is a fixed number in the interval [1,2].…”
Section: Proof Of Theoremmentioning
confidence: 99%
See 1 more Smart Citation
“…Эти ограничения приводят к существен-но новым явлениям, которые не возникали при аппроксимации функций полианалитическими многочленами общего вида. Эта глава основана на результатах статьи [41].…”
Section: главаunclassified
“…In Baranova et al (2016), the authors consider an interesting analogous problem: find necessary and sufficient conditions so that P (K) + P (K)z n is dense in A(K) + A(K)z n . The paper obtained some results for a Caratheodory compact set K with n ≥ 2 (see Baranova et al (2016), Theorem 1).…”
Section: Introductionmentioning
confidence: 99%