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981.
M.S. Asgari 《Journal of Mathematical Analysis and Applications》2005,308(2):541-553
In this paper we develop the frame theory of subspaces for separable Hilbert spaces. We will show that for every Parseval frame of subspaces {Wi}i∈I for a Hilbert space H, there exists a Hilbert space K⊇H and an orthonormal basis of subspaces {Ni}i∈I for K such that Wi=P(Ni), where P is the orthogonal projection of K onto H. We introduce a new definition of atomic resolution of the identity in Hilbert spaces. In particular, we define an atomic resolution operator for an atomic resolution of the identity, which even yield a reconstruction formula. 相似文献
982.
We prove Sobolev-type p(⋅)→q(⋅)-theorems for the Riesz potential operator Iα in the weighted Lebesgue generalized spaces Lp(⋅)(Rn,ρ) with the variable exponent p(x) and a two-parametrical power weight fixed to an arbitrary finite point and to infinity, as well as similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces Lp(⋅)(Sn,ρ) on the unit sphere Sn in Rn+1. 相似文献
983.
Michel Mehrenberger 《Acta Mathematica Hungarica》2004,103(4):321-348
By applying the theory of semigroups, we generalize an earlier result of Komornik and Loreti [5] on the observability of compactly
perturbed systems. As an application, we answer a question of the same authors concerning the observability of weakly coupled
linear distributed systems.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
984.
S. P. Gavrilov S. I. Tarapov A. A. Vertiy M. E. Özel 《International Journal of Infrared and Millimeter Waves》1996,17(10):1719-1734
The problem deals with the evolution of the electromagnetic field inside resonator with the paramagnetic filling is considered. The complex magnetic susceptibility obtained from the Bloch equations has been presented in a form of power series intensity of the electromagnetic field. The solution of evolution equations describing the time dependence of the electromagnetic field inside the resonator under the conditions of harmonical excitation is obtained. 相似文献
985.
Wen-Chi Kuo 《Journal of Mathematical Analysis and Applications》2005,303(2):509-521
Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation operators on Riesz spaces are shown to be averaging operators. Here the theory of f-algebras is used when defining multiplication on the Riesz spaces. This leads to the extension of these conditional expectation operators to their so-called natural domains, i.e., maximal domains for which the operators are both averaging operators and conditional expectations. The natural domain is in many aspects analogous to L1. 相似文献
986.
Rudolf Beran 《Annals of the Institute of Statistical Mathematics》2002,54(4):900-917
Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk. 相似文献
987.
Mathematical Notes - 相似文献
988.
989.
Wei Cai 《Advances in Computational Mathematics》2002,16(2-3):157-174
In this paper, we will address three computational issues for electromagnetic scattering in layered media: fast algorithm of calculating dyadic Green's functions, high order RWG current basis and fast solver for layered media. Numerical results will be included. 相似文献
990.
Eugene S. Kryachko Antnio J. C. Varandas 《International journal of quantum chemistry》2002,89(4):255-259
Some new properties of the nonadiabatic coupling elements are derived, in particular the orthogonality and gauge invariance of their longitudinal and transverse components. A method for constructing a strictly diabatic basis set that makes both the transverse and longitudinal components of the nonadiabatic coupling elements of the two‐state problem vanish identically and is based on introducing overlap between the electronic states in the vicinity of the crossing seam is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 相似文献