Universal Taylor Series on products of planar domains

Kioulafa, K.; Kotsovolis, Giorgos; Nestoridis, Vassili

doi:10.48550/arxiv.1909.03521

Cited by 2 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In section 2 we give some preliminary results concerning A D (K). In section 3 we extend to several variables [1], [11] and [14]. In section 4 we strengthen the result of section 2 obtaining approximation for all derivatives.…”

Section: Introductionsupporting

confidence: 55%

“…Remark 4.8. For Universal Taylor series with parameters with respect to many enumerations, we refer to Remark 3.8 and Section 6 of [11]. where n = 1, 2, .…”

Section: MImentioning

confidence: 99%

“…In [1] we consider families of universal Taylor series depending on a parameter; then the function h to be approximated by the partial sums can depend on the same parameter. This led to functions of several complex variables; see also [4], [5], [11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal Taylor Series in several variables depending on parameters

Giorgos¹,

Maronikolakis²,

Nestoridis³

2020

Preprint

View full text Add to dashboard Cite

We establish generic existence of Universal Taylor Series on products Ω = Ω i of planar simply connected domains Ω i where the universal approximation holds on products K of planar compact sets with connected complements provided K ∩Ω = ∅. These classes are with respect to one or several centers of expansion and the universal approximation is at the level of functions or at the level of all derivatives. Also, the universal functions can be smooth up to the boundary, provided that K ∩ Ω = ∅ and {∞} ∪ [C \ Ω i ] is connected for all i. All previous kinds of universal series may depend on some parameters; then the approximable functions may depend on the same parameters, as it is shown in the present paper. These universalities are topologically and algebraically generic.

show abstract

Section: Introductionsupporting

confidence: 55%

“…Remark 4.8. For Universal Taylor series with parameters with respect to many enumerations, we refer to Remark 3.8 and Section 6 of [11]. where n = 1, 2, .…”

Section: MImentioning

confidence: 99%

See 1 more Smart Citation

Universal Taylor Series in several variables depending on parameters

Giorgos¹,

Maronikolakis²,

Nestoridis³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The answer to this question is negative. The proof is similar to a result in Section 6 of [4]. where K i ⊆ C are compact with C \ K i connected for all i = 1, .…”

Section: The Algebra a D (L)mentioning

confidence: 61%

Universal power series of Seleznev with parameters in several variables

Maronikolakis¹,

Stamatiou²

2020

Preprint

View full text Add to dashboard Cite

We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on products K = d i=1 K i , where K i ⊆ C are compact sets and C \ K i are connected, i = 1, . . . , d and 0 / ∈ K. On such K the partial sums approximate uniformly any polynomial. Finally, the partial sums may be replaced by more general expressions. The phenomenon is topologically and algebraically generic.

show abstract

Universal Taylor Series on products of planar domains

Cited by 2 publications

References 17 publications

Universal Taylor Series in several variables depending on parameters

Universal Taylor Series in several variables depending on parameters

Universal power series of Seleznev with parameters in several variables

Contact Info

Product

Resources

About