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A SPECTRAL CHARACTERIZATION OF ALMOST PERIODIC FUNCTIONS ON MOORE GROUPS

A. I. Shtern
장전수학회 (Jangjeon Mathematical Society)|2015.01|Advanced Studies in Contemporary Mathematics|제25권 제1호|pp. 147-150

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참고문헌

키워드

compact groupinvariant meandual space of a locally compact groupbounded uniformly continuous functionalmost periodic functionspectral characterization
주제분류수학

초록

It is proved that every uniformly continuous function on an [FIR] locally compact group (i.e., a group all of whose irreducible representations are finite-dimensional) is almost periodic provided that its spectrum is discrete.

Abstract

It is proved that every uniformly continuous function on an [FIR] locally compact group (i.e., a group all of whose irreducible representations are finite-dimensional) is almost periodic provided that its spectrum is discrete.

참고문헌 (12)

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  3. A. G. Baskakov, "Spectral tests for the almost periodicity of the solutions of functional equations", Mat. Zametki, 24(2), pp.195~206 (1978)
  4. W. Arendt, "Discrete spectrum and almost periodicity", Taiwanese J. Math, 3(4), pp.475~490 (1999)
  5. C. C. Moore, "Groups with finite dimensional irreducible representations", Trans. Amer. Math. Soc, 166, pp.401~410 (1972)
  6. L. C. Robertson, "A note on the structure of Moore groups", Bull. Amer. Math. Soc, 75, pp.594~599 (1969)
  7. A. I. ˇStern, "Locally bicompact groups with finite-dimensional irreducible representations", Mat. Sb, 90(132), pp.86~95 (1973)
  8. E. Hewitt, "Abstract Harmonic Analysis. Vol. I" (1979), Springer-Verlag
  9. A. Beurling, "On the spectral synthesis of bounded functions", Acta Math, 81, pp.225~238 (1948)
  10. J. Dixmier, "Les C¤-algebres et leurs representations" (1969), Gauthier-Villars Editeur
  11. M. A. Naimark, "Normed Algebras, Izdat" (1972), Wolters-Noordhoff Publishing
  12. K. Hartmann, "Pedersen ideal and group algebras", Proc. Amer. Math. Soc, 83(1), pp.183~188 (1981)

관련 논문AI추천

A FORMULA FOR THE INVARIANT MEAN ON THE WEAK ALMOST PERIODIC FUNCTIONS ON MOORE GROUPSA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호CONTINUITY CONDITIONS FOR LOCALLY BOUNDED FINITE-DIMENSIONAL REPRESENTATIONS OF TOTALLY DISCONNECTED LOCALLY COMPACT GROUPSA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호CONTINUITY CONDITIONS FOR LOCALLY BOUNDED FINITE-DIMENSIONAL REPRESENTATIONS OF ALMOST CONNECTED LOCALLY COMPACT GROUPSA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제4호Automatic continuity of locally bounded pseudocharacters on connected locally compact groupsA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제4호CONNECTED LOCALLY COMPACT GROUPS HAVING SUFFICIENTLY MANY FINITE-DIMENSIONAL LINEAR REPRESENTATIONSAlexander I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제1호Finite-dimensional finally precontinuous unitary pseudorepresentations of almost connected locally compact groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제3호

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