Extension operators for spaces of infinite differentiable Whitney jets

Frerick, Leonhard

doi:10.1515/crelle.2007.005

Cited by 28 publications

(51 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further information can be found in [15]. (1) There exists a continuous and linear extension operator T : and a k = a k (Hf ) are the Fourier coefficients of Hf .…”

Section: Examplementioning

confidence: 99%

Shrinking and boundedly complete Schauder frames in Fréchet spaces

Bonet

Fernández

Galbis

et al. 2014

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

ElsevierBonet Solves, JA.; Fernandez, C.; Galbis, A.; Ribera Puchades, JM. (2014) AbstractWe study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

show abstract

“…Further information can be found in [15]. (1) There exists a continuous and linear extension operator T : and a k = a k (Hf ) are the Fourier coefficients of Hf .…”

Section: Examplementioning

confidence: 99%

Shrinking and boundedly complete Schauder frames in Fréchet spaces

Bonet

Fernández

Galbis

et al. 2014

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Since γ i is defined as the distance between supp(ϕ i ) and K and this is equal to dist(supp(ϕ i ), x i ), condition (3) from Lemma 1 ensures that γ i dist(x, K) |x − x i | 3γ i for all x ∈ supp(ϕ i ). So using the Leibniz rule and the other properties of the ϕ i we find constants C (2) k and C (3) …”

Section: Construction Of the Tame Linear Extension Operatormentioning

confidence: 99%

“…There is a vast amount of literature about the question whether one can choose the extension to depend in a good way on the jet, we only mention the articles [1][2][3][4][5][6]8]. Whitney [9] himself proved that one can extend jets of finite order by a continuous linear operator (if E n (K) is endowed with its natural Banach space topology).…”

Section: Introductionmentioning

confidence: 99%

Tame linear extension operators for smooth Whitney functions

Frerick

Jordá

Wengenroth

2011

Journal of Functional Analysis

Self Cite

View full text Add to dashboard Cite

For a compact set K ⊆ R d we present a rather easy construction of a linear extension operator E : E (K) → C ∞ (R d ) for the space of Whitney jets E (K) which satisfies linear tame continuity estimateswhere · s denotes the s-th Whitney norm. The construction turns out to be possible if and only if the local Markov inequality LMI(s) introduced by Bos and Milman holds for every s > r on K. In particular, E (K) admits a tame linear extension operator if and only if the local Markov inequality LMI(s) holds on K for some s 1.

show abstract

“…For spaces of test functions and distributions, we use the notation of Schwartz in [17] and Horváth in [10]. For spaces of Whitney functions, we use the notation of Frerick in [8] and of Vogt in [24]. For tensor product topologies, we follow the notation of Schwartz' treatise on vector-valued distributions [16, pp.…”

mentioning

confidence: 99%

Completing the Valdivia–Vogt tables of sequence-space representations of spaces of smooth functions and distributions

Bargetz

2014

Monatsh Math

View full text Add to dashboard Cite

In the Valdivia-Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1-10, 2013) there are two gaps. We fill in these gaps by proving the representations D F ∼ = s ⊗ π C (N) andḂ ∼ = s ⊗c 0 , where D F is a pre-dual space of the space of distributions of finite order introduced by J. Horváth and the spaceḂ is the space of distributions vanishing at infinity introduced by L. Schwartz.

show abstract

Extension operators for spaces of infinite differentiable Whitney jets

Cited by 28 publications

References 20 publications

Shrinking and boundedly complete Schauder frames in Fréchet spaces

Shrinking and boundedly complete Schauder frames in Fréchet spaces

Tame linear extension operators for smooth Whitney functions

Completing the Valdivia–Vogt tables of sequence-space representations of spaces of smooth functions and distributions

Contact Info

Product

Resources

About