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1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
Jean-Paul Bézivin 《Aequationes Mathematicae》1992,43(2-3):159-176
Summary In this paper, we study the convergence of formal power series solutions of functional equations of the formP
k(x)([k](x))=(x), where
[k]
(x) denotes thek-th iterate of the function.We obtain results similar to the results of Malgrange and Ramis for formal solutions of differential equations: if(0) = 0, and(0) =q is a nonzero complex number with absolute value less than one then, if(x)=a(n)x
n is a divergent solution, there exists a positive real numbers such that the power seriesa(n)q
sn(n+1)2
x
n has a finite and nonzero radius of convergence. 相似文献
10.
Mario Bonk 《Aequationes Mathematicae》1997,53(1-2):54-72
Summary In this paper we solve the functional equationx(u + v)(u – v) = f
1(u)g1(v) + f2(u)g2(v) under the assumption thatx, , f
1, f2, g1, g2 are complex-valued functions onR
n
,n N arbitrary, and 0 and 0 are continuous. Our main result shows that, apart from degeneracy and some obvious modifications, theta functions of one complex variable are the only continuous solutions of this functional equation. 相似文献
11.
Dr. Paul Ressel 《manuscripta mathematica》1975,16(1):47-49
A function : [0, )(-,0] is the logarithm of the Laplace transform of an infinitely divisible probability measure on [0,) if and only if (0)=0, is continuous and conditionally positiv semi-definite. 相似文献
12.
Maria Moszyńska 《Geometriae Dedicata》2000,83(1-3):131-147
Let
be a family of star bodies in R
n
(compact bodies in R
n
with nonempty kernels). A function s:
R
n
is a selector for
provided that s(A) ker A for every A
. To every star body A and every : [0,) [0,) we assign a function A: ker A R defined in terms of the radial function of translates of A. We prove that if A is convex and is concave and strictly increasing, then
A
has a unique maximizer, which is referred to as the radial center of A induced by (Theorem 3.1). We extend the radial center map over some family of star bodies (Theorem 4.2). Further, we define a suitable metric,
st
, the star metric, on the family of all the compact star sets in R
n
. This new metric is topologically stronger than the Hausdorff metric (Theorem 5.7). We study the continuity of our selectors with respect to
st
. 相似文献
13.
V. L. Velikin 《Mathematical Notes》1970,8(1):492-495
An investigation of the approximation on [0, 1] of functionsf (x) by spline functions s(f,; x) of degree 2r-1 and of deficiency r (r>1) depending on the vector function =
1 (x),...,
r-1(x) and interpolatingf (x) at fixed points. For the optimal choice of the vector
0, exact estimates are obtained of the norms f(x)-s (f,
0; x)C[0,1] and f (x)-s (f,
0; x)L[0, 1] on the function classes H
Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 41–46, July, 1970.In conclusion we would like to thank N. P. Korneichuk for suggesting this problem and for his valuable advice. 相似文献
14.
K. Kh. Boimatov 《Mathematical Notes》1973,14(4):837-839
It is proved that if(x) is the majorant of the s-numbers of a completely continuous operator A (i.e.,'(x)- 0, Sn(A) (n)) and if there are found numbers [0, 1] and r0 > 0 such that r0
(r)/(r) will be monotonic in (r0,), then for some > 0,((x) will be a majorant of the eigenvalues of A.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 487–492, October, 1973. 相似文献
15.
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
16.
Piotr Bugiel 《Monatshefte für Mathematik》1992,113(4):255-263
A class of uniformly expanding, piecewiseC
2-diffeomorphisms from domainsIR
d
(bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix (P
)={gG:Pg=g} whereP
is the Frobenius-Perron operator associated with andG={gL
1: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence {P
j
g} is convergent inL
1 for anygG, and in the topology of uniform convergence for anygG(1). The limit is a linear projectionR inL
1 (defined by (3.1)) which mapsG onto Fix (P
) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday 相似文献
17.
Xiaodong Zhou 《Applied Mathematics and Optimization》1992,25(3):263-285
We study the parabolic problemu/t=divx p() in the function space L2(0, T; BV()). Here is the linear growth functional arising from the study of plastic antiplanar shear deformations. 相似文献
18.
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
19.
In this paper solutions in series form for the stresses due to a nucleus of thermo-elastic strain in an infinite elastic solid in the presence of a spherical cavity and also in an elastic solid sphere have been found.
Nomenclature x, y, z Cartesian coordinates; - r, , spherical polar coordinates; - u x ,u y ,u z components of displacement in Cartesian coordinates; - u r ,u ,u components of displacement in spherical coordinates; - r , , , , r , components of stress in spherical coordinates; - E coefficient of elasticity in stress; - G coefficient of elasticity in shear; - coefficient of linear expansion; - Poisson's ration The following nomenclature has been used in this paper: 相似文献
Zusammenfassung Die thermischen Spannungen in einem festen Körper unendlicher Ausdehnung, welcher einen sphärischen Hohlraum enthält, sind bei einer Temperatur von 0°C in Gegenwart eines erhitzten Elementes, das sich in endlichem Abstand vom Hohlraum befindet, hergeleitet worden, wobei zahlenmässige Angaben für die Spannungen und Verschiebungen an der Oberfläche des Hohlraums gemacht werden können. Die Ergebnisse sind mit den entsprechenden, für den zweidimensionalen Fall gültigen Zahlenwerten verglichen worden. Ferner was es möglich, auch für das Problem einer festen Kugel von der Temperatur 0°C und einem erhitzten Kern in ihrem Innern eine Lösung zu finden.
Nomenclature x, y, z Cartesian coordinates; - r, , spherical polar coordinates; - u x ,u y ,u z components of displacement in Cartesian coordinates; - u r ,u ,u components of displacement in spherical coordinates; - r , , , , r , components of stress in spherical coordinates; - E coefficient of elasticity in stress; - G coefficient of elasticity in shear; - coefficient of linear expansion; - Poisson's ration The following nomenclature has been used in this paper: 相似文献
20.
N. S. Faour 《Acta Mathematica Hungarica》1999,84(3):237-243
Let D be the open unit disk in C, and L
h
2
the space of quadratic integrable harmonic functions defined on D. Let
be a function in L(D) with the property that (b) = lim
x
b,xD (x) for all b D. Define the operator C on L
h
2
as follows: C(f) = Q( · f), where Q is the orthogonal projection of L2(D) onto L
h
2
. In this paper it is shown that if C is Fredholm, then is bounded away from zero on a neighborhood of D. Also, if C is compact, then |D 0, and the commutator ideal of (D) is K(D), where (D) denotes the norm closed subalgebra of the algebra of all bounded operators on L
h
2
generated by
, and K(D) is the ideal of compact operators on L
h
2
. Finally, the spectrum of classes of operators defined on L
h
2
is characterized. 相似文献