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961.
Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Πm leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Πm for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Πm+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered. 相似文献
962.
Jinsung Park 《Journal of Functional Analysis》2009,257(6):1713-1758
In this paper we derive a relationship of the leading coefficient of the Laurent expansion of the Ruelle zeta function at s=0 and the analytic torsion for hyperbolic manifolds with cusps. Here, the analytic torsion is defined by a certain regularized trace following Melrose [R.B. Melrose, The Atiyah-Patodi-Singer Index Theorem, Res. Notes Math., vol. 4, A.K. Peters, Ltd., Wellesley, MA, 1993]. This extends the result of Fried, which was proved for the compact case in [D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Invent. Math. 84 (3) (1986) 523-540], to a noncompact case. 相似文献
963.
In this article we prove new results concerning the existence and various properties of an evolution system UA+B(t,s)0?s?t?T generated by the sum −(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express UA+B(t,s)0?s?t?T as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by −A(t) and −B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D⊂?t∈[0,T]D(A(t)+B(t)) everywhere dense in B. We obtain a special case of our formula when B(t)=0, which, in effect, allows us to reconstruct UA(t,s)0?s?t?T very simply in terms of the semigroup generated by −A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of time-dependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrödinger type in quantum mechanics. 相似文献
964.
We construct higher order spectral shift functions, extending the perturbation theory results of M.G. Krein [M.G. Krein, On a trace formula in perturbation theory, Mat. Sb. 33 (1953) 597-626 (in Russian)] and L.S. Koplienko [L.S. Koplienko, Trace formula for perturbations of nonnuclear type, Sibirsk. Mat. Zh. 25 (1984) 62-71 (in Russian); translation in: Trace formula for nontrace-class perturbations, Siberian Math. J. 25 (1984) 735-743] on representations for the remainders of the first and second order Taylor-type approximations of operator functions. The higher order spectral shift functions represent the remainders of higher order Taylor-type approximations; they can be expressed recursively via the lower order (in particular, Krein's and Koplienko's) ones. We also obtain higher order spectral averaging formulas generalizing the Birman-Solomyak spectral averaging formula. The results are obtained in the semi-finite von Neumann algebra setting, with the perturbation taken in the Hilbert-Schmidt class of the algebra. 相似文献
965.
Robin Nittka 《Journal of Functional Analysis》2009,257(5):1429-1444
We consider the Laplacian ΔR subject to Robin boundary conditions on the space , where Ω is a smooth, bounded, open subset of RN. It is known that ΔR generates an analytic contraction semigroup. We show how this semigroup can be obtained from the Gaussian semigroup on C0(RN) via a Trotter formula. As the main ingredient, we construct a positive, contractive, linear extension operator Eβ from to C0(RN) which maps an operator core for ΔR into the domain of the generator of the Gaussian semigroup. 相似文献
966.
Kre?n's formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Kre?n's formula. 相似文献
967.
Zhixiang Wu 《Acta Appl Math》2009,106(2):185-198
In present paper we define a new kind of weak quantized enveloping algebra
of Borcherds superalgebras
. It is a noncommutative and noncocommutative weak graded Hopf algebra. Using localizing with some Ore set, we obtain a different
kind of quantized enveloping algebras of Borcherds superalgebras
. It has a homomorphic image which is isomorphic to the usual quantum enveloping algebra
of
. Moreover,
is isomorphic to a direct sum of
and an other algebra as algebras.
The author is sponsored by ZJNSF No. Y607136. 相似文献
968.
The perturbation of the generator of a Borel right process by a signed measure is investigated, using probabilistic and analytic
potential theoretical methods. We establish a Feynman-Kac formula associated with measures charging no polar set and belonging
to an extended Kato class. A main tool of this approach is the validity of a Khas’minskii Lemma for Stieltjes exponentials
of positive left continuous additive functionals.
相似文献
969.
Simpson校正公式 总被引:3,自引:1,他引:2
给出了Simpson校正公式的截断误差,分析了复化Simpson校正公式的收敛阶.数值算例验证了理论分析的正确性. 相似文献
970.
常息力更新场合有限时间破产概率对负相依索赔额的不敏感性 总被引:1,自引:0,他引:1
江涛 《高校应用数学学报(A辑)》2009,24(4)
设索赔来到过程为具有常数利息力度的更新风险模型.在索赔额分布为负相依的次指数分布假定下,建立了有限时间破产概率的一个渐近等价公式.所得结果显示,在独立同分布索赔额情形,有限时间破产概率的有关渐近等价公式,在负相依场合依然成立.这表明有限时间破产概率对于索赔额的负相依结构是不敏感的. 相似文献