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991.
Ferenc Móricz 《Acta Mathematica Hungarica》2008,120(4):355-366
We introduce the higher order Lipschitz classes Λ
r
(α) and λ
r
(α) of periodic functions by means of the rth order difference operator, where r = 1, 2, ..., and 0 < α ≦ r. We study the smoothness property of a function f with absolutely convergent Fourier series and give best possible sufficient conditions in terms of its Fourier coefficients
in order that f belongs to one of the above classes.
This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192. 相似文献
992.
We study the L
p
-saturation for the linear combination of Bernstein-Kantorovich operators. As a result we obtain the saturation class by using
K-functional as well as some modulus of smoothness.
Research supported by National Natural Science Foundation of China (10671019) and Zhejiang Provincial Natural Science Foundation
of China (102005). 相似文献
993.
Let H
1, H
2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H
1 and taking values in H
2. In this article we prove the following results:
We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results. 相似文献
(i) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H 1 = H 2 and T is self-adjoint, then |
(ii) | inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)} |
(iii) | Every isolated spectral value of T is an eigenvalue of T |
(iv) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T |
(v) | σ(T) bounded implies T is bounded. |
994.
Haïkel Skhiri 《Journal of Mathematical Analysis and Applications》2009,358(2):320-326
Let B(H) be the algebra of all bounded linear operators on a complex infinite-dimensional Hilbert space H. For every T∈B(H), let m(T) and q(T) denote the minimum modulus and surjectivity modulus of T respectively. Let ?:B(H)→B(H) be a surjective linear map. In this paper, we prove that the following assertions are equivalent:
- (i)
- m(T)=m(?(T)) for all T∈B(H),
- (ii)
- q(T)=q(?(T)) for all T∈B(H),
- (iii)
- there exist two unitary operators U,V∈B(H) such that ?(T)=UTV for all T∈B(H).
995.
M. B. Sikhov 《Russian Mathematics (Iz VUZ)》2009,53(8):69-71
We obtain a criterion for embedding the class SH p Ω into that SB q,? Ω* (1 < p ≤ q < ∞). We also determine the exact order of the best approximations of functions from classes SB p,? Ω by trigonometric polynomials whose harmonics belong to sets generated by level surfaces of the majorant Λ (t). 相似文献
996.
If the vector space of all regular operators between the vector lattices E and F is ordered by the collection of its positive operators, then the Dedekind completeness of F is a sufficient condition for to be a vector lattice. and some of its subspaces might be vector lattices also in a more general situation. In the paper we deal with ordered vector
spaces of linear operators and ask under which conditions are they vector lattices, lattice-subspaces of the ordered vector space
or, in the case that is a vector lattice, sublattices or even Banach lattices when equipped with the regular norm. The answer is affirmative for
many classes of operators such as compact, weakly compact, regular AM-compact, regular Dunford-Pettis operators and others if acting between appropriate Banach lattices. Then it is possible to
study the finite elements in such vector lattices , where F is not necessary Dedekind complete. In the last part of the paper there will be considered the question how the order structures
of E, F and are mutually related. It is also shown that those rank one and finite rank operators, which are constructed by means of finite
elements from E′ and F, are finite elements in . The paper contains also some generalization of results obtained for the case in [10].
相似文献
997.
George Darsavelidze Domenti Gabunia Zurab Zoidze Jimsher Tsikaridze 《Journal of solid state chemistry》2004,177(2):605-608
Effect of doping with Zr(Re) on the structure and physical-mechanical properties of β-rhombohedral boron has been studied. In all specimens p-type conductivity was found. Internal friction and dynamic shear modulus of the specimens were investigated at frequencies of torsion oscillations (0.5-5 Hz) in the temperature range 80<T<1000 K. The increase of Zr(Re) concentration in the samples results in increase of their hole concentration, this increasing and shifting the observed IF maxima to lower temperatures; activation energy of the maxima and frequency factor of the relaxation processes decrease by 10-15%. Effects of change of the structure-sensitive properties observed in Zr-(Re)-doped boron are analyzed in view of changes of activation energy necessary for the motion of twinning boundaries and stacking faults. 相似文献
998.
Daniyal M. Israfilov 《Czechoslovak Mathematical Journal》2004,54(3):751-765
Let L C be a regular Jordan curve. In this work, the approximation properties of the p-Faber-Laurent rational series expansions in the weighted Lebesgue spaces L
p(L, ) are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a kth integral modulus of continuity in L
p(L, ) spaces is estimated. 相似文献
999.
The form and sizes of the particles of cellulose-containing disperse systems obtained by dry grinding or dispersing in water a source material (wood pulp and sawdust), destructed by the thermocatalytic method, have been investigated. Their physicochemical and rheological (for aqueous dispersions) properties as well as the physicomechanical properties of composites based on such systems have been studied. By dry grinding, a powder of microcrystalline cellulose (MCC) (in the case of wood pulp) and technical powder (in the case of sawdust) containing particles of sizes from 3 to 20 m were obtained. By dispersing in an aqueous medium the wood pulp destructed to the levelling-off degree of polymerization (LODP), MCC dispersions containing separate microcrystallites and their aggregates were obtained. In the case of their sufficiently high concentration ( 8%), MCC gels having rheological properties typical of liquid-crystalline polymers were formed. It is shown that the cellulose-containing disperse systems obtained may be useful in composites made with polymer materials for improving their strength properties. 相似文献
1000.
Radu Păltănea 《Journal of Computational Analysis and Applications》2003,5(2):195-235
We obtained that for any n N, C = 1 is the smallest constant for which the inequality ||B
n
(f) - f|| C 2(f, 1/n) holds on the class of continuous functions f, as well as on the class of bounded functions f, where B
n
is the Bernstein operators of degree n, 2 is the second order modulus and || || is the sup-norm. 相似文献