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R. Oinarov 《Siberian Mathematical Journal》2007,48(5):884-896
We introduce some nested classes of Volterra type integral operators. For the operators of these classes we establish criteria for boundedness and compactness in Lebesgue spaces. 相似文献
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Árpád Bényi Diego Maldonado Virginia Naibo Rodolfo H. Torres 《Integral Equations and Operator Theory》2010,67(3):341-364
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón–Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well. 相似文献
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We construct the functional calculus for full operators with discrete spectrum over Banach spaces in the interpolation classes
of symbols associated with given operators. We describe new classes of full operators in Banach spaces.
Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998 pp. 127–135. 相似文献
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S. ter Horst M. Messerschmidt A.C.M. Ran M. Roelands M. Wortel 《Indagationes Mathematicae》2018,29(5):1350-1361
In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators. 相似文献
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The idea of symmetric anti-eigenvalue and symmetric anti-eigenvector of a bounded linear operator T on a Hilbert space H is introduced. The structure of symmetric anti-eigenvectors of a self-adjoint and certain classes of normal operators is found in terms of eigenvectors. The Kantorovich inequality for self-adjoint operators and bounds for symmetric anti-eigenvalues for certain classes of normal operators are also discussed. 相似文献
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In this paper, we introduce the class of almost weak* Dunford–Pettis operators and give a characterization of this class of operators. We study its relation with the classes of weak* Dunford–Pettis operators and almost Dunford–Pettis operators, and its relation with the closely related classes of almost limited operators and L-weakly compact operators. 相似文献
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《Mathematische Nachrichten》2017,290(5-6):738-755
We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes. 相似文献
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V.A. Yurko 《Applied Mathematics Letters》2013,26(4):506-509
Generalizations of the classical Ambarzumyan theorem are provided for wide classes of self-adjoint differential operators with arbitrary self-adjoint boundary conditions: scalar Sturm–Liouville operators, higher-order differential operators, matrix Sturm–Liouville operators and operators on spatial networks. 相似文献
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Among the Carleman operators on Banach lattices, we consider the operators that are decomposition operators or lattice homormphisms. Using a generalization of an atom, characterizations for these two classes of operators on Banach lattices with order units are provided. 相似文献
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本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间.给出了广义周期Besov类的一种推广,得到了空间元素的一种表示定理,不仅给出了一种多元周期多项式样条算子.而且证明了所得的结果. 相似文献
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A. A. Esin 《Mathematical Notes》2008,83(5-6):594-603
A classical theorem of Post [1] describes five precomplete classes in the set of Boolean functions. In [2], it was shown that there exist 18 precomplete classes of functions of three-valued logic. In [1, 2], the closure of sets of functions with respect to the substitution operator was studied. We consider two closure operators on functions of three-valued logic, which are obtained by supplementing the substitution operator by closures with respect to two identifications of function values, and prove the existence of three precomplete classes for one of these operators and five precomplete classes for the other. 相似文献
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We study self-adjoint operators in Krein space. Our goal is to show that there is a relationship between the following classes of operators: operators with a compact “corner,” definitizable operators, operators of classes (H) and K(H), and operators of class D κ +. 相似文献
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We construct examples which distinguish clearly the classes of p-hyponormal operators for 0<p?∞. In addition, we show that those examples classify the classes of w-hyponormal, absolute-p-paranormal, and normaloid operators on the complex Hilbert space. Only a few examples of p-hyponormal operators have been examined. Our technique can provide many examples related to the above operators. 相似文献
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Geraldo Botelho 《Linear and Multilinear Algebra》2017,65(6):1232-1246
The usual techniques to generate ideals of multilinear operators between Banach spaces fail in generating hyper-ideals in general. In this paper, we fill this gap by developing two techniques to generate hyper-ideals of multilinear operators. The techniques we develop generate new classes of multilinear operators and show that some important well-studied classes are Banach or p-Banach hyper-ideals. 相似文献
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Higher even order linear differential operators with unbounded coefficients are studied. For these operators the eigenvalues of the characteristic polynomials fall into distinct classes or clusters. Consequently the spectral properties, deficiency indices and spectra, of the underlying differential operators are superpositions of the contributions from the individual clusters. These results are based on a quantitative improvement of Levinson's Theorem. Our methods will also be applicable to other classes of linear differential operators. 相似文献
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Some uniqueness theorems on the least eigenvalue are provided for wide classes of self-adjoint operators: differential operators with operator-valued potentials, higher-order partial differential operators and the p-Laplacian. 相似文献
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We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we establish some alternative characterizations for the class of Cohen strongly summing multilinear operators. 相似文献