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991.
Extensions for Sobolev mappings between manifolds 总被引:1,自引:0,他引:1
We consider two compact Riemannian manifoldsM andN, such thatM has a boundary (but notN). We address the extension problem in the Sobolev class, namely, we investigate the question: foru W
1–1/p,pM,N is there a mapV inW
1/p(M,N) such thatV=u on M. Various results are given, and an emphasis is put on the special (simple) caseN=S
1. 相似文献
992.
A functional integral representation is given for a large class of quantum mechanical models with a non-L
2 ground state. As a prototype, the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state on the Weyl algebra, and a functional measure (spectral stochastic process) is constructed on trajectories taking values in the spectrum of the maximal Abelian subalgebra of the Weyl algebra isomorphic to the algebra of almost periodic functions. The thermodynamical limit of the finite-volume functional integrals for such models is discussed, and the superselection sectors associated to an observable subalgebra of the Weyl algebra are described in terms of boundary conditions and/or topological terms in the finite-volume measures.Supported by DFG, Nr. Al 374/1-2 相似文献
993.
Multidimensional constant linear systems 总被引:10,自引:0,他引:10
Ulrich Oberst 《Acta Appl Math》1990,20(1-2):1-175
A continuous resp. discrete r-dimensional (r1) system is the solution space of a system of linear partial differential resp. difference equations with constant coefficients for a vector of functions or distributions in r variables resp. of r-fold indexed sequences. Although such linear systems, both multidimensional and multivariable, have been used and studied in analysis and algebra for a long time, for instance by Ehrenpreis et al. thirty years ago, these systems have only recently been recognized as objects of special significance for system theory and for technical applications. Their introduction in this context in the discrete one-dimensional (r=1) case is due to J. C. Willems. The main duality theorem of this paper establishes a categorical duality between these multidimensional systems and finitely generated modules over the polynomial algebra in r indeterminates by making use of deep results in the areas of partial differential equations, several complex variables and algebra. This duality theorem makes many notions and theorems from algebra available for system theoretic considerations. This strategy is pursued here in several directions and is similar to the use of polynomial algebra in the standard one-dimensional theory, but mathematically more difficult. The following subjects are treated: input-output structures of systems and their transfer matrix, signal flow spaces and graphs of systems and block diagrams, transfer equivalence and (minimal) realizations, controllability and observability, rank singularities and their connection with the integral respresentation theorem, invertible systems, the constructive solution of the Cauchy problem and convolutional transfer operators for discrete systems. Several constructions on the basis of the Gröbner basis algorithms are executed. The connections with other approaches to multidimensional systems are established as far as possible (to the author).Partially supported by US Air Force Grant AFOSR-87-0249 and by Office of Naval Research Grant N 00014-86-K-0538 through the Center for Mathematical System Theory, University of Florida, Gainesville, Florida, U.S.A. 相似文献
994.
The lattice of monotonely Cauchy (=pre-Lebesgue) locally solid topologies on a given lattice-ordered group is studied. Indentifying topologies agreeing on order bounded sets this lattice becomes a complete Boolean algebra isomorphic to the subalgebra of the lattice's complemented members and realizable as a Boolean algebra of order projections. Some consequences of these results are indicated.Work done while Tim Traynor was visiting professor at University of Napoli sponsored by CNR-Italia. 相似文献
995.
《Electroanalysis》2004,16(8):656-660
For [PMo12O40]3?, the presence of Li+ produced a two‐electron wave at nearly the same potential as the first one‐electron wave in acetonitrile or acetone. The voltammetric behavior of [PMo12O40]3? in a binary mixture of acetonitrile and solvent S was compared with those in a mixture of acetone and S. When the donor number (DN) of S>20, the first two‐electron wave was converted into one‐electron waves in such binary mixtures. The conversion occurred at lower mole fractions of S in an acetonitrile+S mixture than in an acetone+S mixture. The 7Li NMR results showed that the preferential solvating ability of Li+ with S was greater in the former mixture. A linear relationship was found between the iso‐solvation point xiso(S) and the reciprocal of the difference between the DNs of S and acetonitrile, which gave the basis to explain the anomalies observed for a mixture of acetonitrile and H2O. 相似文献
996.
John S. Lew 《Aequationes Mathematicae》1989,38(2-3):146-154
Summary A recent note of Ih-Ching Hsu poses an unsolved problem, to wit, the general solution of the functional equation g(x1, x2) + g(1(x1), 2(x2)) = g(x1, 2(x2)) + g(1(x1),x2), where the i are given functions. This short paper obtains the general solution. It gives conditions which imply that anycontinuous solution has form g1(x1) + g2(x2). 相似文献
997.
B. Nagy 《Periodica Mathematica Hungarica》1980,11(1):1-6
The various essential spectra of a linear operator have been surveyed byB. Gramsch andD. Lay [4]. In this paper we characterize the essential spectra and the related quantities nullity, defect, ascent and descent of bounded spectral operators. It is shown that a number of these spectra coincide in the case of a spectral or a scalar type operator. Some results known for normal operators in Hilbert space are extended to spectral operators in Banach space. 相似文献
998.
Marcin E. Kuczma 《Aequationes Mathematicae》1993,45(2-3):300-321
Summary Homogeneous symmetric meansµ and
, defined on
+
n
and
+
n+1
, respectively, are calledcompatible if the value of
remains unchanged upon replacing n of its arguments by theirµ-mean. Power means (of a common exponent) are a model example, which turns out to be unique, given analyticity of at least one of the two means considered. This is proved by fixing all but one argument in both and
, which leads to a functional equation with two unknown functions, involving their mutual superpositions. The equation is solved in the class of analytic functions by comparing the power series coefficients. 相似文献
999.
Jaak Peetre 《Rendiconti del Circolo Matematico di Palermo》1993,42(2):181-194
We compare two kinds of Hankel type operators, the “BJP-operators” introduced by Boman—Janson—Peetre and the “Z-operators”
considered by Zhang. We show that every BJP-operator comes as an orthogonal sum ofZ-operators. 相似文献
1000.