منابع مشابه
A Generalization of the Rudin-carleson Theorem
The purpose of this paper is to prove a common generalization of a theorem due to T. W. Gamelin [3] and a theorem due to Z. Semadeni [5]. Both these results are generalizations of E. Bishop's abstract version of the well-known RudinCarleson theorem [2]. In the following X denotes a compact Hausdorff space, F a closed subset of X and C(A') and C(F) denote the spaces of all complex-valued functio...
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By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues to hold for such functions. Theorem 1.1 is intimately related to almost everywhere convergence of partial Fourier sums for functions in L[0, 1]. Via a transference principle [12], it is indeed equiv...
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Proof. Let 11 and V be countable bases for X and Y, respectively, and let 3 have as sub-base the collection of sets {fCC(X, Y) \f(U) C V), with UCM and VCÜ. Then 3 certainly has a countable base. Clearly 3 also makes (/, x)—>/(x) jointly continuous, and hence [l, p. 223] is finer than the compact-open topology. Finally, every subset of C(X, Y) is certainly Lindelöf and separable for the countab...
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Carleson's proof of this theorem involves a difficult covering argument and the consideration of a certain quadratic form (see also [ l ] ) . L. Hörmander later found a proof which appeals to the Marcinkiewicz interpolation theorem and avoids any discussion of quadratic forms. The main difficulty in this approach is to show that a certain sublinear operator is of weak type (1, 1). Here a coveri...
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In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1962
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1962-0133462-4