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51.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
52.
In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\). 相似文献
53.
In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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Numerical Algorithms - The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions... 相似文献
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B. Roussière E. Le Blanc G. Savard H. T. Duong J. Pinard S. Liberman J. K. P. Lee J. E. Crawford G. Thekkadath P. Kilcher J. Obert J. Oms J. C. Putaux J. Sauvage ISOCELE Collaboration 《Hyperfine Interactions》1988,43(1-4):473-476
Isotope shift (IS) and hyperfine structure (HFS) measurements have been performed for185, 187, 189, 191, 195Pt using the PILIS (Post ISOCELE Laser Isobar Separator) apparatus installed at the ISOCELE facility. Magnetic and quadrupole
moments have been deduced from the HFS results. The charge radius changes determined for these odd nuclei from the IS results,
added to the σ<r2> values of the even-A nuclei are compared to the results of lattice Hartree-Fock+BCS calculations for asymmetric solutions:185Pt is confirmed to be prolate shaped whereas187, 189, 191Pt are likely triaxial in their ground states. 相似文献
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In this paper we calculate some effective cross-sections of leptons on the basis of S-matrix constructed in 8-dimensional united space [1]. The Lagrangian is chosen, within the framework of the 0 (71) group classification of elementary particles. Electromagnetic interaction does not change the internal structure of the participating particles. The results obtained agree well with experiments. 相似文献
60.
We give criteria for the Cohen-Macaulay and Gorenstein property of Rees algebras of height 2 non-singular equimultiple prime
ideals in terms of explicite representations of the associated graded rings. As consequences, we show that in general, the
Cohen-Macaulay resp. Gorenstein property of such Rees algebras does not imply the Cohen-Macaulay resp. Gorenstein property
of the base ring and that these properties depend upon the characteristic.
Dedicated to the memrory of Professor Lê Van Thiêm
Professor Lê Van Thiêm was the first directorof Hanoi Institute of Mathematics 相似文献