Absolutely Representing Systems of Exponentials in the Spaces of Infinitely-Differentiable Functions and Extendability in the Sense of Whitney

Yu. F. KOROBEINIK

Article Details

Absolutely Representing Systems of Exponentials in the Spaces of Infinitely-Differentiable Functions and Extendability in the Sense of Whitney

Authors:

Yu. F. KOROBEINIK

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2001 Vol.25 Issue 4, pp.503-518

Document Type:

Article

Publication Date:

3/2001

Document Language:

Turkish

Document ID (Org No.):

2000749037

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

Let Q be a compactum in~\mathbb{R}p, p\geqslant1,  such that int  Q\neq\varnothing and Q=\overline{ int  Q}.  Denote by C\infty[Q] the space of functions from  C\infty( int Q) uniformly continuous in  int  Q  together with all their partial derivatives.  The conditions of the  existence of absolutely representing systems of exponentials with  purely imaginary exponents in the space C\infty[Q] and some of its  subspaces of Denjoy--Carleman type are investigated.  It is also  proved under rather general assumptions that there is no such  absolutely representing systems in the space  E(G)=\operatornamewithlimits{proj}\limits {\overleftarrow {Q\in  \mathcal{F}G}}E[Q] where G is an arbitrary open set  in~\mathbb{R}p, E[Q] is C\infty[Q] or its subspace mentioned  above and \mathcal{F}G is the totality of all non-empty compact  sets \mathcal{K} in G with the property \mathcal{K}=  \overline{ int \mathcal{K}}.

 

Let Q be a compactum in~\mathbb{R}p, p\geqslant1,  such that int  Q\neq\varnothing and Q=\overline{ int  Q}.  Denote by C\infty[Q] the space of functions from  C\infty( int Q) uniformly continuous in  int  Q  together with all their partial derivatives.  The conditions of the  existence of absolutely representing systems of exponentials with  purely imaginary exponents in the space C\infty[Q] and some of its  subspaces of Denjoy--Carleman type are investigated.  It is also  proved under rather general assumptions that there is no such  absolutely representing systems in the space  E(G)=\operatornamewithlimits{proj}\limits {\overleftarrow {Q\in  \mathcal{F}G}}E[Q] where G is an arbitrary open set  in~\mathbb{R}p, E[Q] is C\infty[Q] or its subspace mentioned  above and \mathcal{F}G is the totality of all non-empty compact  sets \mathcal{K} in G with the property \mathcal{K}=  \overline{ int \mathcal{K}}.

Article Details

Absolutely Representing Systems of Exponentials in the Spaces of Infinitely-Differentiable Functions and Extendability in the Sense of Whitney

Authors:

Yu. F. KOROBEINIK

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2001 Vol.25 Issue 4, pp.503-518

Document Type:

Article

Publication Date:

3/2001

Document Language:

Turkish

Document ID (Org No.):

2000749037

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

25

(2001)

503-518. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.25

iss.4.

Issues

Article Details

Absolutely Representing Systems of Exponentials in the Spaces of Infinitely-Differentiable Functions and Extendability in the Sense of Whitney

Authors: Yu. F. KOROBEINIK

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2001 Vol.25 Issue 4, pp.503-518

Document Type: Article

Publication Date: 3/2001

Document Language: Turkish

Document ID (Org No.): 2000749037

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

25

(2001)

503-518. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.25

iss.4.

Issues

Authors:

Yu. F. KOROBEINIK

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2001 Vol.25 Issue 4, pp.503-518

Document Type:

Article

Publication Date:

3/2001

Document Language:

Turkish

Document ID (Org No.):

2000749037

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098