2017
DOI: 10.1007/s13398-017-0424-5
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Splitting and parameter dependence in the category of $$\hbox {PLH}$$ PLH spaces

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Cited by 4 publications
(7 citation statements)
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“…Proposition 25.19, p. 303], there exist n ∈ ℕ and 𝜆 > 0 with M ⊂ 𝜆B n . We derive from (7) that proving the continuity of H.…”
Section: Propositionmentioning
confidence: 90%
See 1 more Smart Citation
“…Proposition 25.19, p. 303], there exist n ∈ ℕ and 𝜆 > 0 with M ⊂ 𝜆B n . We derive from (7) that proving the continuity of H.…”
Section: Propositionmentioning
confidence: 90%
“…The parameter dependence problem for a variety of partial differential operators on several spaces of (generalised) differentiable functions has been extensively studied, see e.g. [4,6,7,16,31,32] and the references and background in [3,22]. The answer to this problem for the Cauchy-Riemann operator is affirmative since the Cauchy-Riemann operator on the space C ∞ ( , E) of E-valued smooth functions is surjective if E = C ∞ (U) ( O(U) , D(V) � ) by [8, Corollary 3.9, p. 1112] which is a consequence of the splitting theory of Bonet and Domański for PLS-spaces [3,4], the topological isomorphy of C ∞ ( , E) to Schwartz' -product C ∞ ( ) E and the fact that ∶ C ∞ ( ) → C ∞ ( ) is surjective on the nuclear Fréchet space C ∞ ( ) (with its usual topology).…”
Section: Introductionmentioning
confidence: 99%
“…Then the quotient space, equipped with these seminorms, is a locally convex space (but maybe not Hausdorff). Since (7) holds for every representative F of f , we obtain for every…”
Section: Dualitymentioning
confidence: 99%
“…The parameter dependence problem for a variety of partial differential operators on several spaces of (generalised) differentiable functions has been extensively studied, see e.g. [4,6,7,37,38,18] and the references and background in [3,26]. The answer to this problem for the Cauchy-Riemann operator is affirmative since the Cauchy-Riemann operator…”
Section: Introductionmentioning
confidence: 99%
“…The splitting theory of Bonet and Domański can also be applied if F (Ω) is a non-Fréchet PLS-space and for PLH-spaces F (Ω), e.g. D L 2 and B loc 2,κ (Ω) which are non-PLS-spaces, the splitting theory of Dierolf and Sieg [15,16] is available. For applications we refer the reader to the already mentioned papers [4,6,15,16,64,65] as well as [5,18] where F (Ω) is the space of ultradistributions of Beurling type or of ultradifferentiable functions of Roumieu type and E, amongst others, the space of real analytic functions and to [30] where F (Ω) is the space of C ∞ -smooth functions or distributions.…”
Section: Introductionmentioning
confidence: 99%