• 제목/요약/키워드: Locally compact group

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BOCHNER-SCHWARTZ THEOREM ON LOCALLY COMPACT ABELIAN GROUPS

  • Kim, Jin-Man;Cho, Jong-Gyu
    • 대한수학회보
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    • 제38권1호
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    • pp.7-16
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    • 2001
  • We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

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SHIFT GENERATED DUAL FRAMES FOR LOCALLY COMPACT ABELIAN GROUPS

  • Ahmadi, Ahmad;Askari-Hemmat, Ataollah
    • 대한수학회지
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    • 제49권3호
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    • pp.571-583
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    • 2012
  • Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS

  • Gol, Rajab Ali Kamyabi;Tousi, Reihaneh Raisi
    • 대한수학회지
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    • 제48권5호
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    • pp.899-912
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    • 2011
  • We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

ON THE SEPARATING IDEALS OF SOME VECTOR-VALUED GROUP ALGEBRAS

  • Garimella, Ramesh V.
    • 대한수학회보
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    • 제36권4호
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    • pp.737-746
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    • 1999
  • For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

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SOME PROPERTIES ON SPACES WITH NONCOMPACT GROUP ACTION

  • Lee, Hyang-Sook;Shin, Dong-Sun
    • 대한수학회논문집
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    • 제12권3호
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    • pp.717-723
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    • 1997
  • The compact transformation group has been developed with lots of properties. Many properties which are satisfied on G-space for compact group G do not hold for noncompact case. To recover some theory on spaces with noncompact group action we give some restriction on G-spaces. Hence we introduced Cartan G-spaces and proper G-spaces for our goal and we prove some properties on these G-spaces with noncompact G.

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The Universal Property of Inverse Semigroup Equivariant KK-theory

  • Burgstaller, Bernhard
    • Kyungpook Mathematical Journal
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    • 제61권1호
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    • pp.111-137
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    • 2021
  • Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.