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Finite dimensional \(H\)-invariant spaces. (English) Zbl 0894.43001

The authors prove results on \(H\)-invariant subspaces of \(M(G)\), the space of all bounded Radon measures on a locally compact (mainly Abelian) group \(G\) (respectively \(L^\infty (G))\), invariant under certain subsets \(H\) of \(G\), containing only trigonometric polynomials, generalizing results of M. Engert [Pac. J. Math. 32, 333–343 (1970; Zbl 0189.43102)] or L. Székelyhidi [C. R. Math. Acad. Sci., Soc. R. Can. 7, 315–320 (1985; Zbl 0579.42001)]. They also obtain some related results on almost periodic functions.

MSC:

43A10 Measure algebras on groups, semigroups, etc.
43A20 \(L^1\)-algebras on groups, semigroups, etc.
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
22D15 Group algebras of locally compact groups
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References:

[1] DOI: 10.1016/0022-247X(79)90239-7 · Zbl 0426.43002 · doi:10.1016/0022-247X(79)90239-7
[2] DOI: 10.1155/S0161171282000027 · Zbl 0486.43001 · doi:10.1155/S0161171282000027
[3] DOI: 10.2307/2034591 · Zbl 0138.37903 · doi:10.2307/2034591
[4] Szekelyhidi, C.R. Math. Rep. Acad. Sci. 7 pp 315– (1985)
[5] Szekelyhidi, Pacific J. Math. 103 pp 583– (1982) · Zbl 0419.43004 · doi:10.2140/pjm.1982.103.583
[6] DOI: 10.2307/1990290 · Zbl 0032.02901 · doi:10.2307/1990290
[7] DOI: 10.2307/1998197 · Zbl 0417.43006 · doi:10.2307/1998197
[8] Loewner, J. Math. Mech. 8 pp 393– (1959)
[9] Crombez, Colloq. Math. 39 pp 325– (1978)
[10] Graham, Colloq. Math. 55 pp 131– (1988)
[11] Engert, Pacific J. Math. 32 pp 333– (1970) · Zbl 0189.43102 · doi:10.2140/pjm.1970.32.333
[12] Edwards, J. Austral. Math. Soc. 4 pp 403– (1964)
[13] Hewitt, Abstract harmonic analysis I (1963)
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