Translationinvariant linear forms on L\(^2\)(G) for compact Abelian groups G

DOI10.1016/0022-1236(72)90063-8zbMath0247.43004OpenAlexW2029250258MaRDI QIDQ2555995

Gary H. Meisters

Publication date: 1972

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(72)90063-8

Mathematics Subject Classification ID

Harmonic analysis on specific compact groups (43A75) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (18)

Function spaces on the unit circle ⋮ Discontinuous Translation Invariant Functionals ⋮ Translation-invariant linear forms on \({\mathcal E}'(G)\) and non-Liouville tuples on G ⋮ Differences of functions and group generators for compact Abelian groups ⋮ Sharpness results concerning finite differences in Fourier analysis on the circle group ⋮ The Mathematical Work of Wolfgang Schmidt ⋮ Vanishing Fourier Transforms and Generalized Differences in ⋮ A remark on discontinuous translation invariant functionals on \(L_ p (G)\) for certain compact groups \(G\) ⋮ Topologically invariant linear forms on spaces of abstract distributions on a locally compact Abelian group ⋮ Vanishing Fourier coefficients and the expression of functions in \(L^2(\mathbb{T})\) as sums of generalised differences ⋮ Periodic distributions and non-Liouville numbers ⋮ Discontinuous translation-invariant linear forms on \(\mathcal K(G)\) ⋮ Non-Liouville numbers and a theorem of Hörmander ⋮ Banach spaces of functions and distributions characterized by singular integrals involving the Fourier transform ⋮ A remark on continuity of translation invariant functionals on \(L_ p(G)\) for compact Lie groups G ⋮ Uniqueness of translation invariant norms ⋮ Continuity of linear operators commuting with shifts ⋮ Translation invariant forms on \(L^ p(G)\) \((1<p<\infty)\)

Cites Work

• Simultaneous approximation to algebraic numbers by rationals
• Translation-invariant linear forms and a formula for the Dirac measure
• Some discontinuous translation-invariant linear forms
• Translation-invariant linear forms and a formula for the Dirac measure
• On a Problem of Heilbronn†

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