共查询到20条相似文献,搜索用时 15 毫秒
1.
Suppose that f is the characteristic function of a probability measure on the real line \(\mathbb R\). In this paper, we deal with the following problem posed by N.G. Ushakov: Is it true that f is never determined by its imaginary part \(\mathfrak {I}f\)? In other words, is it true that for any characteristic function f there exists a characteristic function g such that \(\mathfrak {I}f\equiv \mathfrak {I}g\) but \( f\not \equiv g\)? We study this question in the more general case of the characteristic function defined on an arbitrary locally compact abelian group. A characterization of what characteristic functions are uniquely determined by their imaginary parts are given. As a consequence of this characterization, we obtain that several frequently used characteristic functions on the classical locally compact abelian groups are uniquely determined by their imaginary parts. 相似文献
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The classical edge-of-the-wedge theorem for holomorphic functions is generally false for CR functions. However, it is true
on Levi-indefinite hypersurfaces for wedges pointing in null directions. 相似文献
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Dedicated to the memory of S.K. Pichorides 相似文献
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L. Kuntz 《Journal of Optimization Theory and Applications》1995,86(1):263-270
A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1). 相似文献
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T. N. Saburova 《Mathematical Notes》1975,18(3):800-806
We prove a theorem giving necessary and sufficient conditions for embedding the class Lip 1 in a class of functions which is defined in terms of the absolute convergence of series of Fourier coefficients with respect to the Faber-Schauder system, normalized in L2. 相似文献
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V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
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Let be a pseudoconvex domain and let be a locally pluriregular set, . Put
Let be an open neighborhood of and let be a relatively closed subset of . For let be the set of all for which the fiber is not pluripolar. Assume that are pluripolar. Put
Then there exists a relatively closed pluripolar subset of the ``envelope of holomorphy' of such that:
Let be an open neighborhood of and let be a relatively closed subset of . For let be the set of all for which the fiber is not pluripolar. Assume that are pluripolar. Put
Then there exists a relatively closed pluripolar subset of the ``envelope of holomorphy' of such that:
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for every function separately holomorphic on there exists exactly one function holomorphic on with on , and
is singular with respect to the family of all functions .
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I. E. Chyzhykov 《Proceedings of the American Mathematical Society》2002,130(2):517-528
We obtain a sharp asymptotic relation between the infimum and the maximum on a circle of a subharmonic function of zero lower order. An example is constructed, which shows the sharpness of the relation in the class of entire functions of zero order such that , where as .
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Meng-Kuang Kuo 《数学物理学报(B辑英文版)》2011,31(3):1203-1212
The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences (see [5]). In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R~2+ . 相似文献
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V. Rao 《Mathematical Notes》1968,3(3):159-162
If the boundary values of a function, harmonic in a sphere, and its normal derivative decrease sufficiently fast to zero as a fixed point of the sphere is approached, then the corresponding function is identically zero. This note gives an unimprovable condition on the rate of decrease for which the stated uniqueness theorem holds.Translated from Matematicheskie Zametki, Vol. 3, No. 3, pp. 247–252, March, 1968. 相似文献
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András Biró 《Acta Mathematica Hungarica》2012,135(4):350-382
We prove that a relatively general even function f(x) (satisfying a vanishing condition, and also some analyticity and growth conditions) on the real line can be expanded in
terms of a certain function series closely related to the Wilson functions introduced by Groenevelt in 2003. The coefficients
in the expansion of f will be inner products in a suitable Hilbert space of f and some polynomials closely related to Wilson polynomials (these are well-known hypergeometric orthogonal polynomials). 相似文献
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《Optimization》2012,61(4):397-400
We give a simple and direct proof, using lower semicontinuous functions, of a generalization of the open mapping theorem for metrizable topological vector spaces (that are not necessarily locally convex) and operators with complete graph. Our result is in a form more applicable to applied (convex) analysis. 相似文献
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Risto Korhonen 《Journal of Mathematical Analysis and Applications》2009,357(1):244-253
A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order. As a corollary of this result it is shown that if n∈N and three distinct values of a meromorphic function f of hyper-order less than 1/n2 have forward invariant pre-images with respect to a fixed branch of the algebraic function τ(z)=z+αn−1z1−1/n+?+α1z1/n+α0 with constant coefficients, then f○τ≡f. This is a generalization of Picard's theorem for meromorphic functions of small hyper-order, since the (empty) pre-images of the usual Picard exceptional values are special cases of forward invariant pre-images. 相似文献