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Degenerate $C$-ultradistribution semigroups in locally convex spaces

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Marko Kostić, Stevan Pilipović, Daniel Velinov

Functional Analysis · Submitted 10 Oct 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The main subject in this paper are degenerate $C$-ultradistribution semigroups in barreled sequentially complete locally convex spaces.

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arXiv ID1610.02788 (version 1)
Pith IDSI5XHQYC, Pith's permanent record of this paper and its review
CitationDaniel Velinov, Marko Kosti\'c, Stevan Pilipovi\'c. "Degenerate $C$-ultradistribution semigroups in locally convex spaces." arXiv:1610.02788 (2016). https://pith.science/paper/SI5XHQYC
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arXiv listing abstract v1. Results and the main claim are underlined; .

The main subject in this paper are degenerate $C$-ultradistribution semigroups in barreled sequentially complete locally convex spaces. Here, the regularizing operator $C$ is not necessarily injective and the infinitesimal generator is multivalued linear operator. We also consider exponential degenerate $C$-ultradistribution semigroups.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 The main subject in this paper are degenerate $C$-ultradistribution semigroups in barreled sequentially complete locally convex spaces. contribution 0.80 0.30 0.11 asserted 0.99
s1 Here, the regularizing operator $C$ is not necessarily injective and the infinitesimal generator is multivalued linear operator. contribution 0.76 0.31 0.08 asserted 0.94
s2 We also consider exponential degenerate $C$-ultradistribution semigroups. contribution 1.00 0.76 0.06 asserted 0.95

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The main subject in this paper are degenerate $C$-ultradistribution semigroups in barreled sequentially complete locally convex spaces. Here, the regularizing operator $C$ is not necessarily injective and the infinitesimal generator is multivalued linear operator. We also consider exponential degenerate $C$-ultradistribution semigroups.

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  • If $𝐆$ is a (C-DCF) in $E$ ((C-UDCF) of $∗$-class in $E$), then $ℬ$ is single-valued and we can proceed as in the proof of [ref] so as to conclude that $𝐆(·)𝐀⊆𝐀𝐆(·).$ Combining this fact with Proposition [ref], [ref] and [ref] and the arguments contained in the proof of Theorem [ref], we get that $𝐆$ is a (C-DCF) in $E$ ((C-UDCF) of $∗$-class in $E$) generated by $𝐀$ iff $𝒢$ is a ($𝒞$-DS) in $E⊕E$ (($𝒞$-UDS) of $∗$-class in $E⊕E$) generated by $𝒜.$ This is an extension of [ref] .

    Degenerate $C$-distribution cosine functions and degenerate $C$-ultradistribution cosine functions in locally convex spaces · The basic properties of degenerate $C$-distribution cosine functions and degenerate $C$-ultradistribution cosine functio · 0.93

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