On a property of PLS-spaces inherited by their tensor products

Piszczek, Krzysztof

doi:10.36045/bbms/1267798505

Cited by 9 publications

(8 citation statements)

References 3 publications

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“…Remark. Results on inheritance of dual interpolation estimates for Schwartz (tensor) products of PLS-spaces were very recently obtained by Piszczek using the results of this paper, see [67].…”

Section: Proposition 53 If a Pair Of Pls-spacesmentioning

confidence: 71%

Real analytic parameter dependence of solutions of differential equations

Domański¹

2010

Rev. Mat. Iberoam.

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We consider the problem of real analytic parameter dependence of solutions of the linear partial differential equation P (D)u = f , i.e., the question if for every family (f λ) ⊆ D (Ω) of distributions depending in a real analytic way on λ ∈ U , U a real analytic manifold, there is a family of solutions (u λ) ⊆ D (Ω) also depending analytically on λ such that P (D)u λ = f λ for every λ ∈ U,

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Section: Proposition 53 If a Pair Of Pls-spacesmentioning

confidence: 71%

Real analytic parameter dependence of solutions of differential equations

Domański¹

2010

Rev. Mat. Iberoam.

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“…Domański showed the above result under the additional assumption that the space X is so called deeply reduced. By [29,Prop. 8] this assumption is superfluous.…”

Section: Lemma 52 [19 Lemma 112]mentioning

confidence: 99%

Solution to the first Cousin problem for vector-valued quasianalytic functions

Debrouwere

Vindas

2017

Annali di Matematica

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“…Piszczek for several helpful conversations and especially for discussions on their papers [6], [13].…”

Section: Acknowledgements the Author Is Very Indebted To Pawe L Domamentioning

confidence: 99%

On the algebra of smooth operators

Ciaś

2013

Studia Math.

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Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s ′ , s) of the so-called smooth operators. We also characterize closed commutative * -subalgebras of L(s ′ , s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN ) of s.1 2010 Mathematics Subject Classification. Primary: 46H35, 46J25, 46H30. Secondary: 46H15, 46K10, 46A11, 46L05.Key words and phrases: Topological algebras of operators, topological algebras with involution, representations of commutative topological algebras, functional calculus in topological algebras, nuclear Fréchet spaces, C *algebras, smooth operators, space of rapidly decreasing smooth functions.

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On a property of PLS-spaces inherited by their tensor products

Cited by 9 publications

References 3 publications

Real analytic parameter dependence of solutions of differential equations

Real analytic parameter dependence of solutions of differential equations

Solution to the first Cousin problem for vector-valued quasianalytic functions

On the algebra of smooth operators

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