Examples of compact sets with non-empty interior which do not admit a continuous linear extension operator for ultradifferentiable functions of Beurling type

1994 ◽  
Vol 62 (3) ◽  
pp. 239-247 ◽  
Author(s):  
Uwe Franken
Keyword(s):  
Linear Extension ◽  
Extension Operator ◽  
Continuous Linear ◽  
Compact Sets ◽  
Empty Interior ◽  
Ultradifferentiable Functions ◽  
Linear Extension Operator

scholarly journals A linear extension operator for Whitney fields on closed o-minimal sets

2008 ◽  
Vol 58 (2) ◽  
pp. 383-404
Author(s):  
Wiesław Pawłucki
Keyword(s):  
Linear Extension ◽  
Extension Operator ◽  
Minimal Sets ◽  
Linear Extension Operator

Continuous Linear Extension of Ultradifferentiable Functions of Beurling Type

1993 ◽  
Vol 164 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Uwe Franken
Keyword(s):  
Linear Extension ◽  
Continuous Linear ◽  
Ultradifferentiable Functions

scholarly journals Extension operators for Sobolev spaces commuting with a given transform

1998 ◽  
Vol 40 (2) ◽  
pp. 291-296 ◽  
Author(s):  
Viktor Burenkov ◽  
Bert-Wolfgang Schulze ◽  
Nikolai N. Tarkhanov
Keyword(s):  
Real Axis ◽  
Sobolev Spaces ◽  
Linear Extension ◽  
Extension Operator ◽  
Bounded Linear ◽  
The Real ◽  
Linear Extension Operator

AbstractWe consider a real-valued function r = M(t) on the real axis, such that M(t) < 0 for t < 0. Under appropriate assumptions on M, the pull-back operator M* gives rise to a transform of Sobolev spaces Ws.p (-∞, 0) that restricts to a transform of Ws.p(-∞, ∞). We construct a bounded linear extension operator Ws.p(-∞, 0) → Ws.p(−∞, ∞), commuting with this transform.

scholarly journals A bounded linear extension operator for L^(2,p)(R^2)

2013 ◽  
Vol 178 (1) ◽  
pp. 183-230 ◽  
Author(s):  
Arie Israel
Keyword(s):  
Linear Extension ◽  
Extension Operator ◽  
Bounded Linear ◽  
Linear Extension Operator

Linear Extension Operators for Ultradifferentiable Functions of Beurling Type on Compact Sets

1989 ◽  
Vol 111 (2) ◽  
pp. 309 ◽  
Author(s):  
Reinhold Meise ◽  
B. Alan Taylor
Keyword(s):  
Linear Extension ◽  
Compact Sets ◽  
Ultradifferentiable Functions

WHITNEY'S TYPE THEOREMS FOR INFINITE DIMENSIONAL SPACES

2000 ◽  
Vol 03 (01) ◽  
pp. 141-160
Author(s):  
S. A. SHKARIN
Keyword(s):  
Linear Extension ◽  
Linear Subspace ◽  
Extension Operator ◽  
Fréchet Space ◽  
Frechet Space ◽  
Entire Space ◽  
Closed Linear Subspace ◽  
Infinite Dimensional ◽  
Class C ◽  
Linear Extension Operator

It is proved that for any f ∈ Ck(L,ℝ), where k ∈ ℕ and L is a closed linear subspace of a nuclear Frechét space X, the function f can be extended to a function of class Ck-1 defined on the entire space X. It is also proved that for any f ∈ Ck (L, ℝ), where k ∈ℕ∪{∞} and L is a closed linear subspace of a conjugate X of a nuclear Frechét space, the function f can be extended to a function of class Ck defined on the entire space X. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

scholarly journals OPERATORS THAT ARE NUCLEAR WHENEVER THEY ARE NUCLEAR FOR A LARGER RANGE SPACE

2004 ◽  
Vol 47 (3) ◽  
pp. 679-694 ◽  
Author(s):  
Eve Oja
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Linear Extension ◽  
Approximation Property ◽  
Closed Subspace ◽  
Extension Operator ◽  
Range Space ◽  
Bounded Linear ◽  
Linear Extension Operator

AbstractLet $X$ be a Banach space and let $Y$ be a closed subspace of a Banach space $Z$. The following theorem is proved. Assume that $X^*$ or $Z^*$ has the approximation property. If there exists a bounded linear extension operator from $Y^*$ to $Z^*$, then any bounded linear operator $T:X\rightarrow Y$ is nuclear whenever $T$ is nuclear from $X$ to $Z$. The particular case of the theorem with $Z=Y^{**}$ is due to Grothendieck and Oja and Reinov. Numerous applications are presented. For instance, it is shown that a bounded linear operator $T$ from an arbitrary Banach space $X$ to an $\mathcal{L}_\infty$-space $Y$ is nuclear whenever $T$ is nuclear from $X$ to some Banach space $Z$ containing $Y$ as a subspace.AMS 2000 Mathematics subject classification: Primary 46B20; 46B28; 47B10

The Whitney problem of existence of a linear extension operator

1997 ◽  
Vol 7 (4) ◽  
pp. 515-574 ◽  
Author(s):  
Yuri Brudnyi ◽  
Pavel Shvartsman
Keyword(s):  
Linear Extension ◽  
Extension Operator ◽  
Linear Extension Operator

The wavelet transform on spaces of type S

2006 ◽  
Vol 136 (4) ◽  
pp. 837-850 ◽  
Author(s):  
R. S. Pathak ◽  
S. K. Singh
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
The Other ◽  
Continuous Wavelet ◽  
Continuous Linear ◽  
Ultradifferentiable Functions ◽  
Linear Map ◽  
The One

The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S. It is shown that, for wavelets belonging to the one type of S-space defined on R, the wavelet transform is a continuous linear map of the other type of the S-space into a space of the same type (latter type) defined on R × R+. The wavelet transforms of certain ultradifferentiable functions are also investigated.

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