共查询到20条相似文献,搜索用时 46 毫秒
1.
S. V. Petras 《Journal of Mathematical Sciences》1984,24(3):380-386
The behavior of the poles zn(), n=1,2,... of the scattering matrix of the operatorl
u=–u(x), x , (u/n)+(x)u|=0 as 0 is considered. It is proved that |zn()–zn|=0((1/2)qn), where qn is the order of the pole of the scattering matrix for the operator 0u=–u, u/=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981. 相似文献
2.
J. Tabor 《Aequationes Mathematicae》1990,39(2-3):179-197
Summary Let 0 < 1 and letX, Y be real normed spaces. In this paper we consider the following functional inequality:f(x + y) – f(x) – f(y) min{f(x + y), f(x) + f(y)} forx, y R, wheref: X Y. Mainly continuous solutions are investigated. In the case whereY = R some necessary and some sufficient conditions for this inequality are given.Let 0 <1. The following functional inequality has been considered in [5]:f(x + y) – f(x) – f(y) min{f(x + y), f(x) + f(y)} forx, y R, wheref: R R. It appeared that the solutions of this inequality have properties very similar to those of additive functions (cf. [1], [2], [3]). The inequality under consideration seems to be interesting also because of its physical interpretation (cf. [5]). In this paper we shall consider this inequality in a more general case, wheref is defined on a real normed space and takes its values in another real normed space.The first part of the paper concerns the general case; in the second part we assume that the range off is inR. 相似文献
3.
Klaus-Jürgen Eckardt 《manuscripta mathematica》1976,18(1):43-55
The problem of existence of wave operators for the Klein-Gordon equation (
t
2
–+2+iV1t+V2)u(x,t)=0 (x R
n,t R, n3, >0) is studied where V1 and V2 are symmetric operators in L2(R
n) and it is shown that conditions similar to those of Veseli-Weidmann (Journal Functional Analysis 17, 61–77 (1974)) for a different class of operators are also sufficient for the Klein-Gordon equation. 相似文献
4.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S
V
=
t
V (
t
), where
t
, t Z
, 1, is a Markov Gaussian random field, V Z
, and is a bounded Borel function. We get an estimate from below for the variance of S
V
and construct two classes of functions , for which the LLT of large deviations holds. 相似文献
5.
A subset M of a normed linear space X is called a strict sun if, for any x X\M, the set of its nearest points from M is nonempty and for any point y M which is nearest to x, the point y is a nearest point from M to any point of the ray {x + (1 - )y | > 0\}. We give an intrinsic geometrical characterization of strict suns in the space (n). 相似文献
6.
Prof. Dr. Reinhold Böhme 《manuscripta mathematica》1987,57(2):205-223
Let F denote a surface with boundary F, being contained in a Riemann surface R, such that R\F is somedisk. If we vary the boiundary curve o parametrizing F, we will get a manifold of real dimension 6g–3, such that any bounds some F and any local deformation
of F is conformally equivalent to just one F for .This result also implies that none of the conformal invariants of R will be an invariant of this F, since its neighbors {F|} cover all possible deformations of F at all. 相似文献
7.
We give efficiency estimates for proximal bundle methods for finding f*minXf, where f and X are convex. We show that, for any accuracy <0, these methods find a point xkX such that f(xk)–f* after at most k=O(1/3) objective and subgradient evaluations. 相似文献
8.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K
1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K
1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism. 相似文献
9.
A. Yu. Solynin 《Journal of Mathematical Sciences》2001,105(4):2220-2234
Let D be a simply connected domain on the complex plane such that 0 D. For r > 0 , let D
r be the connected component of D {z : |z| < r} containing the origin. For fixed r, we solve the problem on minimization of the conformal radius R(D
r, 0) among all domains D with given conformal radius R(D, 0). This also leads to the solution of the problem on maximization of the logarithmic capacity of the local -extension E
(a) of E among all continua E with given logarithmic capacity. Here, E
(a) = E {z : |z – a| }, a E, > 0. Bibliography: 12 titles. 相似文献
10.
Gesztesy and Simon recently have proven the existence of the strong resolvent limit A, for A, = A + (·), where A is a self-adjoint positive operator,
being the A-scale). In the present note it is remarked that the operator A, also appears directly as the Friedrichs extension of the symmetric operator
:=A \{f
(A)| f,=0\}. It is also shown that Krein's resolvents formula: (A_b,-z)-1 =(A-z)-1+
(·,
) z, with b=b-(1+z) (z,-1),z= (A-z)-1 defines a self-adjoint operator Ab, for each
and b R1. Moreover it is proven that for any sequence n
which goes to in
there exists a sequence n0 such that
Ab, in the strong resolvent sense. 相似文献
11.
Keiko Kotani 《Annals of Combinatorics》1998,2(2):137-144
LetG be a graph, andk1 an integer. LetU be a subset ofV(G), and letF be a spanning subgraph ofG such that deg
F
(x)=k for allx V(G)–U. If deg
F
(x)k for allxU, thenF is called an upper semi-k-regular factor with defect setU, and if deg
F
(x)k for allxU, thenF is called a lower semi-k-regular factor with defect setU. Now letG=(X, Y;E(G)) be a bipartite graph with bipartition (X,Y) such that X=Yk+2. We prove the following two results.(1) Suppose that for each subsetU
1X such that U
1=max{k+1, X+1/2},G has an upper semi-k-regular factor with defect setU
1Y, and for each subsetU
2Y such that U
2=max{k+1, X+1/2},G has an upper semi-k-regular factor with defect setXU
2. ThenG has ak-factor.(2) Suppose that for each subsetU
1X such that U
1=X–1/k+1,G has a lower semi-k-regular factor with defect setU
1Y, and for each subsetU
2Y such that U
2=X–1/k+1,G has a lower semi-k-regular factor with defect setXU
2. ThenG has ak-factor. 相似文献
12.
Ole Barndorff-Nielsen 《Probability Theory and Related Fields》1969,12(1):56-58
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
13.
Bruce R. Ebanks 《Aequationes Mathematicae》1996,51(1-2):86-99
Summary This paper presents a new, shorter and more direct proof of the following result of J. Aczél and C. T. Ng: IfM: J R (J =]0, 1[
k
) is both multiplicative and additive, then the general solution: J R of(x) + M(1 – x)(y/1 – x) = (y) + M(1 – y)(x/1 – y)
(x, y, x + y J) is given by(x) = ifM = 0,(x) = M(x)[L(x) + ] + M(1 – x)L(1 – x) ifM 0,where is an arbitrary constant andL: J R is an arbitrary solution of the logarithmic functional equationL(xy) = L(x) + L(y) (x, y J).
Also, some extensions of this result to fields more general than the reals are given. 相似文献
14.
Jürgen J. Voss 《Journal of Fourier Analysis and Applications》1999,5(2-3):193-201
It is well known that for certain sequences {tn}n the usual Lp norm ·p in the Paley-Wiener space PW
p
is equivalent to the discrete norm fp,{tn}:=(
n=–
|f(tn)|p)1/p for 1 p = < and f,{tn}:=sup
n|f(tn| for p=). We estimate fp from above by Cfp,
n
and give an explicit value for C depending only on p, , and characteristic parameters of the sequence {tn}n. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer. 相似文献
15.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
16.
The unit sphere of Hilbert space, 2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of 2, (C
i
)
i=1
, and reals
i
0 so that a) each setC
i
has nonempty intersection with every infinite dimensional closed subspace of 2 and b) forij,xC, andyC
j
, |x, y|<min(i, j)
E. Odell was partially supported by NSF and TARP. Th. Schlumprecht was partially supported by NSF and LEQSF. 相似文献
17.
Chih-Wen Weng 《Graphs and Combinatorics》1995,11(2):201-207
LetY = (X, {R
i
}
oid) denote aP-polynomial association scheme. By a kite of lengthi (2 i d) inY, we mean a 4-tuplexyzu (x, y, z, u X) such that(x, y) R
1,(x, z) R
1,(y, z) R
1,(u, y) R
i–1,(u, z) R
i–1,(u, x) R
i. Our main result in this paper is the following. 相似文献
18.
By using the classical Hadamard theorem, we obtain an exact (in a certain sense) inequality for the best polynomial approximations of an analytic function f(z) from the Hardy space H
p, p 1, in disks of radii , 1, and 2, 0 < 1 < < 2 < 1. 相似文献
19.
Laurence A. Bales Ohannes A. Karakashian Steve M. Serbin 《BIT Numerical Mathematics》1988,28(3):651-658
Letr(z) be a rational approximation to cosz with only imaginary poles ±i
1
–1/2
, ±i
2
–1/2
, ..., ±i
m
–1/2
such that |cozz –r(z)| C|z|2m+2 as |z| 0. If the degree of the numerator ofr(z) is less than or equal to 2m and
i m/4,i=1, ...,m, then we show that |r(z)|1 for all realz. 相似文献
20.
Jean-Paul Bézivin 《Aequationes Mathematicae》1992,44(1):84-99
Résumé Soitq un nombre algébrique de module 1, qui ne soit pas une racine de l'unité, etP
[X, Y
0,Y
1] un polynôme non nul. Dans cet article, nous montrons que toute solution de l'équation fonctionnelleP(z, (z), (qz))=0, qui est une série formelle (z) dansQ[[z]], a un rayon de convergence non nul.
Summary Letq Q be an algebraic number of modulus one that is not a root of unity. LetP Q[X, Y 0,Y 1] be a non zero polynomial. In this paper, we show that every formal power series,(z) Q[[z]], solution of the functional equationP(z), (z), (qz)) = 0 has a non zero radius of convergence.相似文献