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1.
A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f:∫+∞∞ |f(t)e-α(t)|pdt +∞},where 1 ≤ p +∞ and α(t) is a weight on R.  相似文献   
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Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   
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C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom ((pq) → (qp)) → (qp). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201-208).  相似文献   
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A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.  相似文献   
5.
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying +∞ ∞ |f(t)| p e -α(t) dt) 1/p ,1 p ∞,and α(t) is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.  相似文献   
6.
Incompleteness and minimality of complex exponential system   总被引:3,自引:0,他引:3  
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series.  相似文献   
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A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lpα = {f: ∫+∞-∞|f(t)e-α(t)|pdt<+∞},where1 ≤ p <+∞ and α(t)is a weight on R.  相似文献   
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