A Projective Description of Generalized Gelfand–Shilov Spaces of Roumieu Type

Debrouwere, Andreas; Vindas, Jasson

doi:10.1007/978-3-030-04459-6_39

Cited by 4 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As classically done, the Roumieu type space S : pR n q could have also be introduced via an inductive limit, and that definition coincides (algebraically and topologically) with the projective description given here (see e.g. [6]). One has that S pMpq pNpq pR n q is an pF Sq-space, while S tMpu tNpu pR n q is pDF Sq.…”

Section: Mppapqmentioning

confidence: 91%

A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

Neyt

Vindas

2019

Integral Transforms and Special Functions

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Mppapqmentioning

confidence: 91%

A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

Neyt

Vindas

2019

Integral Transforms and Special Functions

Self Cite

View full text Add to dashboard Cite

show abstract

“…The author presented that the two classes are equivalent in the sense of Pilipovic and Prangoski, and the conditions presented were based on the use of approximate units. For more details, see recent concerning the quasianalytic case in [2,4].…”

Section: Introductionmentioning

confidence: 99%

Some results on ultradifferential convolution property of ultradistributions

Amaonyeiro,

Isife

2024

AMCS

View full text Add to dashboard Cite

We consider some sequential conditions for the convolvability of two ultradistributions, specifically the Roumieu ultradistributions defined on the space of all ultradifferentiable functions Dn{M_p} in the space Dn'{M_p} and show the similarities between these conditions in the sense of Mincheva-Kaminska S. The sequential conditions are based on the use of approximate identities which satisfy certain conditions to be a Banach algebra for the space Dn{M_p} . We present an equivalent result involving the convolution of the differentiability of two Roumieu ultradistributions with equivalent norm condition.

show abstract

Fourier Characterizations and Non-triviality of Gelfand–Shilov Spaces, with Applications to Toeplitz Operators

Petersson

2023

J Fourier Anal Appl

View full text Add to dashboard Cite

We find growth estimates on functions and their Fourier transforms in the one-parameter Gelfand–Shilov spaces $$S_s$$ S s , $$S^\sigma $$ S σ , $$\Sigma _s$$ Σ s and $$\Sigma ^\sigma $$ Σ σ . We obtain characterizations for these spaces and their duals in terms of estimates of short-time Fourier transforms. We determine conditions on the symbols of Toeplitz operators under which the operators are continuous on the one-parameter spaces. Lastly, it is determined that $$\Sigma _s^\sigma $$ Σ s σ is nontrivial if and only if $$s+\sigma > 1$$ s + σ > 1 .

show abstract

A Projective Description of Generalized Gelfand–Shilov Spaces of Roumieu Type

Cited by 4 publications

References 23 publications

A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

Some results on ultradifferential convolution property of ultradistributions

Fourier Characterizations and Non-triviality of Gelfand–Shilov Spaces, with Applications to Toeplitz Operators

Contact Info

Product

Resources

About