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E. V. Kolesnikov 《Siberian Mathematical Journal》1989,30(5):725-727
Dedicated to Yuri Grigor'evich Reshetnyak on his sixtieth birthday. 相似文献
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Classification of positive solutions to an integral system with the poly-harmonic extension operator
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R~+_n:{u(x)=c_n,a∫_?R_+~n(x_n~(1-a_v)(y)/|x-y|~(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n~(1-a_uθ)(x)/|x-y|~(n-a))dx,y∈ ?R_+~n,where n 2, 2-n a 1, κ, θ 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system. 相似文献
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V. V. Napalkov 《Mathematical Notes》1969,6(4):710-716
A generalized differentiation operator introduced by A. F. Leont'ev is considered in this note. The concept of an LD-operator is introduced, and necessary and sufficient conditions are determined for the extension of a generalized differentiation operator to some LD-operator.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 425–436, October, 1969.The present work was completed under the direction of A. F. Leont'ev to whom the author expresses much gratitude. 相似文献
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M. M. Malamud 《Ukrainian Mathematical Journal》1992,44(2):190-204
Certain classes of extensions of a lacunary Hermitian operator are described in terms of abstract boundary conditions. The connection between the asymptotic behavior of eigenvalues of an extension near the boundary of lacuna and the asymptotic of the negative spectrum of the corresponding boundary operator is found.Candidate of Phisicomathematical Science.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 215–233, February, 1992. 相似文献
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Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z1,z2,…,zn), z1∈D, , pi?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z1),f′(z1)1/p2z2,…,f′(z1)1/pnzn) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z1))1/pi|z1=0=1, i=2,…,n. Some other related results are proved. 相似文献
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In 1995, Roper and Suffridge defined an extension operator which maps a locally biholomorphic function on the unit diskD in ℂ to a locally biholomorphic mapping on the unit ballB
n in ℂn. This extension operator preserves many important properties, e.g., convexity and starlikeness, etc. In this note, we introduce
the family ofε starlike mappings, and prove that the Roper-Suffridge extension operator preserves theε starlikeness on some Reinhardt domains. This result includes many known results and solves an open problem of Graham and
Kohr.
Project supported by the National Science Foundation of China. 相似文献
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D. H. Fremlin 《manuscripta mathematica》1975,15(4):323-327
I give an example of a positive compact operator on L2[0,1] which is not representable by any Lebesgue measurable function on [0,1]2. This example can be adapted to answer a question of H.H.Schaefer (§4 below). 相似文献
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RasulA.Khan 《逼近论及其应用》2002,18(1):90-100
Let C( R ^2) be a class of continuous functions f on R ^2.A bivariate extension Ln(f,x,y)of Bleiman-Butzer-Hahn operator is defined and its standard convergence properties are given.Moreover,a local analogue of Voronovskaja theorem is also give for a subclass of C(R ^2). 相似文献
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Rasul A. Khan 《分析论及其应用》2002,18(1):90-100
Let C(R2+ ) be a class of continuous functions f on R2+. A bivariate extension L.(f ,x,y) of BleimannButzer-Hahn operator is defined and its standard convergence properties are given. Moreover, a local analogue of Voronovskaja theorem is also given for a subclass of C(R2+). 相似文献
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We prove that a linear bounded extension operator exists for the trace of C
1·ω (R
n
)to an arbitrary closed subset of
R
n
.The similar result is obtained for some other spaces of multivariate smooth functions. We also show that unlike the one-dimensional
case treated by Whitney, for some trace spaces of multivariate smooth functions a linear bounded extension operator does not
exist. The proofs are based on a relation between the problem under consideration and a similar problem for Lipschitz spaces
defined on hyperbolic Riemannian manifolds. 相似文献
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We provide a short, elementary proof of the existence and uniqueness of the square root in the context of unbounded positive selfadjoint operators on real or complex Hilbert spaces. 相似文献
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B. A. Ivanov 《Journal of Mathematical Sciences》1980,13(2):216-217
A method is indicated for the approximate determination of the positive eigenvalue of the problem x–Qx=0, >0, xK, x0, whereK is a cone in Banach space and Q is an operator-valued function positive relative toK.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 37–39, 1976. 相似文献