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In a Hubert , with the aid of the postulated Gel'fand-Levitan-Marchenko quantum equations, one introduces the fields 1(x) and 2(x), which are the quantum analogues of the classical fields cosh (x) and sinh (x) in the sinh-Gordon model. It is shown that the fields j(x) satisfy the Wightman axioms, including the invariance relative to reflections of space-time and mutual local commutativity. In addition, one proves the asymptotic completeness of the theory and one computes explicitly the scattering operator. In the developed approach, no cut-offs are used and, therefore, there are no renormalization effects.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 146, pp. 147–190, 1985.  相似文献   

3.
Let t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M n , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d t and, for each x M, we define a smooth real function x (t) : (1 + i (t)), where the i(t) are the eigenvalues of AA T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t , restricted to v at the point x -t M n.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that x ' (t) 0 for all x M and real t; then, if x t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.  相似文献   

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Summary Let P={P : } be an exponential family of probability distributions with the canonical parameter and consider the one to one mapping : P . It is shown that, under mild regularity assumptions, and –1 are continuous with respect to the Lévy metric in P and Euclidean metric in .  相似文献   

6.
LetM t[](x) be the spherical mean value operator applied to a function on a symmetric Riemannian space of the non-compact type.L —decay estimations forM t [](x) as well as for its derivatives with respect to (t, x) are given, provided that belongs to a Banach space with suitable weighted supremum norm. This leads to estimates of the solutions to the wave equation in certain cases in which Huygens' principle is valid.  相似文献   

7.
On Interpolation of the Fourier Maximal Operator in Orlicz Spaces   总被引:1,自引:0,他引:1  
Let and be positive increasing convex functions defined on [0, ). Suppose satisfies the 2-condition, that is, (t)2 (C1t) for sufficiently large t, and has some nice properties. If -1(u)log(u+1) C2-1(u) for sufficiently large uthen we have S*(f) L CfL for all f L ([-, ])where S*(f) is the majorant function of partial sums of trigonometric Fourier series and fL is the Orlicz norm of f. This result is sharp.  相似文献   

8.
Suppose that in a domain R(, B) of variables (r, ): (0 r , 1 +B(r–r 0 ) 2–B(r–r0), where > 0, B > 0, 1 < 0 < 2 are numbers) a metric ds2 = dr2 +G(r, )d 2 and a function k(r, ) are given. The problem of isometrically immersing ds2 in E 4 with prescribed Gaussian torsion is considered. The following is proved: The class C 5 metric ds 2 is locally realized in the form of a class C 3 surface F 2 whose Gaussian torsion is the prescribed class C 3 function (r, ).Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 38–47, 1992.  相似文献   

9.
We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction [0, max] (max is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for 0 and an asymptotic solution for max. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data.  相似文献   

10.
We consider boundary value problems associated with the equation T=–A in a Hilbert Space, where T and A are bounded, self adjoint, injective, and A has a bounded inverse. We discuss the stability of the solution when A is perturbed by a self adjoint operator.  相似文献   

11.
The paper is concerned with Range-Domain Implications MvCvK, where M is a given operator and C,K denote given sets. Sufficient conditions are derived by a very general continuity principle. Various special cases are considered such as inverse-positivity, MvMwvw, and a generalization H(,[,])MvH(,[,]) v, where Mu=H(u,u) and [,] denotes an order interval. These results are applied to differential operators related to boundary or initial value problems. The goal is to furnish a simple uniform approach, to explain its application, and to provide a kind of survey on what problems have been treated in this way.  相似文献   

12.
A jacobi field is understood to be a family (Ã()) of commuting selfadjoint operatorsÃ() acting in a Fock space, having a Jacobi structure, and depending linearly on the test functions . In this article, we give a spectral representation of such a family and outline its applications to the theory of distributions on an infinite dimensional space.This article is dedicated to the memory of my dear teacher Mark G. KreinThe work is partially supported by Fundamental Research Foundation of Ukraine, grant 1.4/62.  相似文献   

13.
Let be a harmonic mapping from a Riemannian 3-manifold to a Riemannian 2-manifold. A smooth function on M is associated to , derived from the eigenvalues of the first fundamental form, the vanishing of which is equivalent to being a harmonic morphism. The Laplacian of this function is computed and a maximum principle applied to derive criteria when a harmonic map must be a harmonic morphism.  相似文献   

14.
In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup of convex characteristic functions on the semiaxis (0,). Letn ()={:1¦11 or 1=}, and Io()={: 1¦ 1 N()}. The following results are proved: 1) The semigroup is almost delphic in the sense of R. Davidson. 2) N() is a set of the type G which is dense in (in the topology of uniform convergence on compacta). 3) The class Io() contains only the function identically equal to one.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 717–725, May, 1977.The author thanks I. V. Ostrovskii for the formulation of the problem and valuable remarks.  相似文献   

15.
In this paper three Banach spacesA 0(),A andA 1() of functions holomorphic in the unit ballB of n are defined. We exhibit bounded projections fromC 0(B) ontoA 0(), fromL 1(B) ontoA 1(), and fromL(B) ontoA(). Using these projections, we show thatA 0()* A 1() andA 1()* A().Supported in part by the National Natural Science Foundation of China.  相似文献   

16.
Summary We consider the Cauchy problem for the generalized porous medium equation ut=(u) where u=u(x, t), xRn and t>0, and the initial datum u(x, 0) is assumed to be nonnegative, integrable mid to nave compact support. The nonlinearity (u) is a C1 function defined for uO which grows like a power of u. Our assumptions generalize the porous medium case, (u)=um, m>1, and also include the equation of the Marshak waves. This problem has finite speed of propagation. We estimate the rate of growth of the support of the solution with precise estimates for t 0 and t. Our main result deals with the regularity of the solutions. We show that after a certain time t0 the pressure, defined by v=(u), with (u)=(u)/u and (0)=0, is a Lipschitz-continuous function of x and t and the interface is a Lipschitz-continuous surface in RN+1; the solution u is Hölder continuous for all times t> 0.Both authors partially supported by CAICYT, Project 2805-83. The second author also supported by USA-Spain Joint Research Grant CCB-8402023.  相似文献   

17.
Summary Approximations for the function implicitly defined by (u)=(u, (u)) are obtained via the iterative scheme n(u)=(u, n–1(u)). In this paper the uniform convergence of high order derivatives of n to the corresponding derivatives of is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.  相似文献   

18.
We study the following variational problem. For a compact manifold S0 embedded in the Euclidean space we consider deformations of S0. They are represented by Lipschitz continuous homeomorphisms of S0 whose images are embedded manifolds. We introduce an energy of a deformation which depends on the first derivative of the curvature of (S0) and the mass of a mass minimizing current which is bounded by (S0). In this paper it is shown that an energy minimizing deformation of (S0) exists. Moreover, in the case that S0 has codimension 1, (S0) is an embedded C3a -submanifold, if is of the class C2,1.  相似文献   

19.
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT L/F ()=1 andTr L/F (i)=i fori=2,...n.  相似文献   

20.
Summary We consider the functional equation(x + y) – (x) – (y) = f(x)f(y)h(x + y) and we find all its homomorphic solutionsf, h, defined in a neighbourhood of the origin.  相似文献   

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