共查询到20条相似文献,搜索用时 78 毫秒
1.
Clasine van Winter 《Integral Equations and Operator Theory》1986,9(3):387-451
Let H(0) be a dilation-analytic three-particle Schrödinger operator with analytic continuation H() (>0). Let a be zero or the energy of a two-particle bound state. Let- (a) be the Laplace operator representing the kinetic energy of the relative motion of fragments scattered in channel a. By recent results, wave operators W (±, a, ) with conjugates W (±, a, ) exist such that W (±, a, ) W (±, a, ) is a projection P (a, ) commuting with H () while [H ()-a]W (±, a, ) equals-W(±, a, ) (a) e2i. This paper shows that the wave operators transform dilation-analytic functions of particle coordinates into dilation-analytic functions. Specifically, if the left shoulder of the spectrum of P (a,) H () does not sweep across eigenvalues of H() when , then W(-, a, ) and W (+, a, ) are dilation analytic in [, ]. If the right shoulder does not sweep across eigenvalues, W(+, a, ) and W(-, a, ) are dilation analytic in [,]. A semisimple eigenvalue of H () embedded in the spectrum of P (a, ) H () does not prevent the wave operators from being dilation analytic in an interval [, ] with as an interior point.This work was supported in part by the National Science Foundation under grant DMS-8301096. 相似文献
2.
Summary Let be thek-dimensional subspace spanned by the translates (·–2j/k),j=0, 1, ...,k–1, of a continuous, piecewise smooth, complexvalued, 2-periodic function . For a given functionfL
2(–, ), its least squares approximantS
kf from can be expressed in terms of an orthonormal basis. Iff is continuous,S
kf can be computed via its discrete analogue by fast Fourier transform. The discrete least squares approximant is used to approximate Fourier coefficients, and this complements the works of Gautschi on attenuation factors. Examples of include the space of trigonometric polynomials where is the de la Valleé Poussin kernel, algebraic polynomial splines where is the periodic B-spline, and trigonometric polynomial splines where is the trigonometric B-spline. 相似文献
3.
S. V. Lapin 《Mathematical Notes》1977,21(5):346-352
For a given -function (u), a condition on a -function (u) is found such that it is necessary and sufficient for the following to hold: if fn(x) f(x) and f
n
(x)M (n=1, 2, ...) where M>0 is an absolute constant, then f
n
(x)–f(x)0(n). An analogous condition for convergence in Orlicz spaces is obtained as a corollary.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 615–626, May, 1977.The author thanks V. A. Skvortsov for his constant attention and guidance on this paper. 相似文献
4.
I. M. Khamitov 《Journal of Mathematical Sciences》1988,40(1):115-148
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
5.
Yurij M. Berezansky 《Integral Equations and Operator Theory》1998,30(2):163-190
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
6.
Tassilo Küpper 《Numerische Mathematik》1976,25(2):201-214
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea
2 and for given functions = we require =C
0[0, 1] C
2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and . 相似文献
7.
M. Lemańczyk 《Probability Theory and Related Fields》1988,78(4):491-507
Summary A new method for construction of transformations T
i: (X
i, B
i,
i) , i=1,2, that are factors of each other but that are not measuretheoretically isomorphic is provided. This method uses ergodic product cocycles of the form S
i
1xS
i
2x...,, where : XZ
2 is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X. 相似文献
8.
Let be a univariant function, and letg(x) be the average of (x,u) asu runs over the unit sphere in
n
. We give a necessary and sufficient condition forg to be a kernel function, i.e., thatg be inL
1 (
n
) and have integral 1. The result is used to give a constructive proof of the density of the ridge functions based upon the function . 相似文献
9.
Alberto Bressan 《Annali di Matematica Pura ed Applicata》1984,137(1):163-173
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
10.
Felicia Bernatzki 《Annals of Global Analysis and Geometry》1997,15(5):379-399
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
11.
B. Z. Shavarovs'kii 《Journal of Mathematical Sciences》1999,96(2):3026-3029
We consider finite sets of numerical matrices and the polynomial matrices corresponding to them that have the Smith form diag (1, (x), ..., (x)). We solve the problem of reducing such sets to canonical form with one similarity transformation assuming that all the roots of the invariant polynomial (x) are simple.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 101–105. 相似文献
12.
L. D. Berkovitz 《Journal of Optimization Theory and Applications》1974,14(5):521-528
A lower closure theorem for an abstract control problem is proved. The functional isJ(,u)=
G
f
0(t, (M)(t),u(t))dt and the state equations areN(t)=f(t, (M)(t),u(t)). It is shown that, if {(
k
,u
k)} is a sequence of admissible controlsu
k and corre-sponding trajectories
k
such that lim infJ(
k
,u
k)<+ and such that
k
weakly,M
k
M strongly,N
k
N weakly, and {u
k} is bounded in someL
p norm, then there is a controlu such that (,u) is admissible and lim infJ(
k
,u
k)J(,u).Dedicated to Professor M. R. HestenesThis research was supported by the National Science Foundation, Grant No. GP-33551X. 相似文献
13.
S. V. Solov'ev 《Journal of Mathematical Sciences》1982,20(4):2367-2369
We consider the (&, )-fragment of the intuitionistic propositional calculus. It is proved that under the standard transformation of a Gentzen derivation into a natural derivation(), the length of (())22·length(
). There is constructed a sequence of Gentzen derivations of length i, for which the length of ((
i))21/3·length(i), which shows that the upper bound obtained is not too weak.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 192–196, 1979. 相似文献
14.
N. L. Pachulia 《Ukrainian Mathematical Journal》1990,42(10):1274-1281
We obtain estimates of (, )-strong integral average deviations of Fourier operators on classes
M defined by A. I. Stepanetz.Translated from Ukrainskii Matematicheskii Zhurnal, Vo. 42, No. 10, pp. 1434–1441, October, 1990. 相似文献
15.
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
16.
H. Kita 《Acta Mathematica Hungarica》1998,81(3):175-193
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
17.
Steven B. Bank 《Annali di Matematica Pura ed Applicata》1992,161(1):83-112
Summary A classical result (see R.Nevanlinna, Acta Math.,58 (1932), p. 345) states that for a second-order linear differential equation, w + P(z) w + Q(z) w=0, where P(z) and Q(z) are polynomials, there exist finitely many rays, arg z=j, for j=1,..., m, such that for any solution w=f(z) 0 and any > 0, all but finitely many zeros off lie in the union of the sectors ¦ arg z - j¦ < for j=1,..., m. In this paper, we give a complete answer to the question of determining when the same result holds for equations of arbitrary order having polynomial coefficients. We prove that for any such equation, one of the following two properties must hold: (a) for any ray, arg z=, and any > 0, there is a solution f 0 of the equation having infinitely many zeros in the sector ¦arg z - ¦ <, or (b) there exist finitely many rays, arg z=j, for j= 1,..., m, such that for any >0, all but finitely many zeros of any solution f 0 must lie in the union of the sectors ¦ arg z - j¦ < for j=1, ..., m. In addition, our method of proof provides an effective procedure for determining which of the two possibilities holds for a given equation, and in the case when (b) holds, our method will produce the rays, arg z=j. We emphasize that our result applies to all equations having polynomial coefficients, without exception. In addition, we mention that if the coefficients are only assumed to be rational functions, our results will still give precise information on the possible location of the bulk of the zeros of any solution.This research was supported in part by the National Science Foundation (DMS-84-20561 and DMS-87-21813). 相似文献
18.
Clasine van Winter 《Integral Equations and Operator Theory》1987,10(1):96-139
This paper starts from a self-adjoint Schrödinger operator H(0) for three particles. If the interaction is dilation-analytic, H(0) has an analytic continuation H() (>0). G(t,) (–(±,a,) defined as strong limits, when t±, of t-dependent operators. The wave operators establish transformations under which the subgroups are similar to unitary groups. The scattering matrix determined by G(t,) is diagonal with respect to a.This work was supported in part by the National Science Foundation under grant DMS-8301096. 相似文献
19.
Summary We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)(f(x) d) A (f(x) d, d d = 1. Iff is an arbitrary nonnegativeL
x
function, this holds if 0, is convex andA = 1. Iff is monotone the measure need not be positive for (J) to hold for all convex withA = 1. If has higher monotonicity, e.g., is also convex, then we get a version of (J) withA < 1 and measures that need not be positive. 相似文献
20.
A. I. Il'inskii 《Mathematical Notes》1977,21(5):400-405
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