A note on positive definite functions
Neil Rickert (1970)
Studia Mathematica
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Neil Rickert (1970)
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A. Hulanicki (1966)
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A. Hulanicki (1964)
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S. Hartman (1964)
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S. Woronowicz (1964)
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Helmut Meyn (1972)
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K. Urbanik (1960)
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María L. Torres de Squire (1993)
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We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φ * f(y) = f (y) almost everywhere for any function f in the space (L, l)(G) (hence in L(G)), 2 ≤ p ≤ ∞, where {φ} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q. ...
E. H. Ostrow, E. M. Stein (1957)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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