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11.
S. A. Shkarin 《Mathematical Notes》2000,67(4):534-540
Both the existence and the nonexistence of a linearly ordered (by certain natural order relations) effective set of comparison
functions (=dense comparison class) are compatible with the ZFC axioms of set theory.
Translated fromMaternaticheskie Zametki, Vol. 67, No. 4, pp. 629–637, April, 2000. 相似文献
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A series is called a pointwise universal trigonometric series if for any , there exists a strictly increasing sequence of positive integers such that converges to f(z) pointwise on . We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as |n|→∞ for some ε>0, then the series Sa cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series Sa with as |n|→∞. 相似文献
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We say that a bounded linear operator T acting on a Banach spaceB is antisupercyclic if for any x B either Tnx = 0 for somepositive integer n or the sequence {Tnx/||Tnx||} weakly convergesto zero in B. Antisupercyclicity of T means that the angle criterionof supercyclicity is not satisfied for T in the strongest possibleway. Normal antisupercyclic operators and antisupercyclic bilateralweighted shifts are characterized. As for the Volterra operator V, it is proved that if 1 p and any f Lp [0,1] then the limit limn (n!||Vnf||p)1/n doesexist and equals 1 inf supp (f). Upon using this asymptoticformula it is proved that the operator V acting on the Banachspace Lp[0,1] is antisupercyclic for any p (1,). The same statementfor p = 1 or p = is false. The analogous results are provedfor operators when the real part of z C is positive. 相似文献
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Stanislav Shkarin 《Journal of Functional Analysis》2010,258(1):132-160
We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set Λ⊆R+×C which is not of zero three-dimensional Lebesgue measure, the family has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if and φ∈H∞(D) is non-constant, then the family has a common hypercyclic vector, where Mφ:H2(D)→H2(D), Mφf=φf, and , providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family has a common hypercyclic vector, where Tbf(z)=f(z−b) acts on the Fréchet space H(C) of entire functions on one complex variable. 相似文献
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Stanislav Shkarin 《Mathematische Annalen》2010,348(2):379-393
A unitary operator V and a rank 2 operator R acting on a Hilbert space H{\mathcal{H}} are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator
can be supercyclic. 相似文献
16.
T. A. Kriger D. V. Tarasova L. M. Plyasova A. V. Shkarin S. S. Stroeva 《Reaction Kinetics and Catalysis Letters》1987,34(1):207-212
Structural transformations of V-P-O catalysts have been studied in situ in oxidative, inert and reducing atmosphere by the high-temperature X-ray diffraction method. Formation of vanadyl phosphates is shown to depend on the P/V ratio in the initial sample. It has been established that transformations in the phase composition of catalysts is independent of the reaction media at P/V=2. The effect of catalyst composition on catalytic properties is discussed.
V-P-O , . , P/V . P/V=2. V-P-O .相似文献
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Stanislav Shkarin 《Journal of Mathematical Analysis and Applications》2008,348(1):193-210
We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T⊕Mg is universal, where Mg is multiplication by a generating element of a compact topological group. We use this result to characterize R+-supercyclic operators and to show that whenever T is a supercyclic operator and z1,…,zn are pairwise different non-zero complex numbers, then the operator z1T⊕?⊕znT is cyclic. The latter answers affirmatively a question of Bayart and Matheron. 相似文献
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19.
Stanislav Shkarin 《Proceedings of the American Mathematical Society》2008,136(5):1659-1670
It is proved that for any separable infinite dimensional Banach space , there is a bounded linear operator on such that satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that satisfies the Kitai criterion for certain backward weighted shifts .
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