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1.
Let XoR n be an irreducible analytic germ and the order space of its field of meromorphicfunetion germs. A formal half-branch in Xo is a kind of C-map germ c[0,)Xo; an ordering is centered at c if it contains the functions which are positive on c. We obtain a partition 1,...,d, d=dim Xo, of the set * of central (i.e.: centered at some half-branch) orderings, according to the dimension of half-branches. Then we show that all e, e= 1,.,d, as well as the set \* of noncentral orderings, are dense in . Finally, we solve the 17th Hubert Problem for analytic germs.  相似文献   

2.
We consider the function space B p l () of functionsf(x), defined on the domain of a certain class and characterized by specific differential-difference properties in Lp(). We prove a theorem on the embedding B p,q l () Lq in the case whenl=n/p –n/q >0 and its generalization for vectorl, p, q.Translated from Matematicheski Zametki, Vol. 6, No. 2, pp. 129–138, August, 1969.  相似文献   

3.
Summary Consider the Dirichlet problem for an elliptic equation in a domain , with coefficients having discontinuity on a surface . Suppose divides into 1 2(2 the inner core), the thickness of 1 is of order of magnitude , and the modulus of ellipticity in 1 is of order magnitude 1. The asymptotic behavior of the solution is studied as 0, 1 0, provided lim (/1) exists. Other questions of this type are studied both for elliptic equations and for elliptic variational inequalities.The second author is partially supported by National Science Foundation Grant 7406375 A01. The third author is partially supported by National Science Foundation Grant MC575-21416 A01.  相似文献   

4.
Letf be analytic in a hyperbolic region . The Bloch constant f off is defined by , where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and where . Then for allf withf() , we have f 1/(). In this paper we study the extremal functions defined by f =1/() and the existence of those functions.Supported by the National Natural Science Foundation of China.  相似文献   

5.
Sato  Ryotaro 《Positivity》1998,2(1):1-18
Let X be a Banach space and (,,µ) be a -finite measure space. We consider a strongly continuous d-dimensional semigroup T={T(u):u=(u1,..., ud, ui >0, 1 i d} of linear contractions on Lp((,,µ); X), with 1 p<. In this paper differentiation theorems are proved for d-dimensional bounded processes in Lp((,,µ); X) which are additive with respect to T. In the theorems below we assume that each T(u) possesses a contraction majorant P(u) defined on Lp((,,µ); R), that is, P(u) is a positive linear contraction on Lp((,,µ); R) such that T(u)f(w) P(u)f(·)() almost everywhere on for all f Lp((,,µ); X).  相似文献   

6.
Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L 2() with generalized Robin boundary conditions where is an arbitrary open subset of R n and is a Borel measure on the boundary of . This operator generates a sub-Markovian C 0-semigroup on L 2(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L p () is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture.  相似文献   

7.
The theory of a matrix-valued function (), j-elementary in the unit circle and having a pole at the point 0, ¦0¦=1, on the boundary of the unit circle, is considered. The structure of () is determined, conditions for the splittingoff of () from an arbitrary matrix-valued function W(), j-expanding in ¦|< 1, are formed, a theorem on the parametrization of a j-elementary matrix-valued function () of full rank is proved, and a decomposition of () of full rank into the product of parametrized j-elementary factors of full rank with simple poles at the point 0 is found.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 62–74, 1988.  相似文献   

8.
Summary This paper studies annihilating properties of operators generated by spherical convolution over the unit sphere 2q of Cq. Its specific aim is to answer the following question: given a complex number , ||1, to determine what functions of L2(2q) have zero average over every section w,q :={ z 2q: <z,w> = } of 2q . Here, <.,.>stands for the usual inner product of Cq.  相似文献   

9.
Let (,A,P) denote some probability space and some sub--algebra ofA. It is shown that there exists a semiregular versionQ (A),A, , of the conditional distributionP(A|), AA, i.e., Q (A), (AA fixed) is andAQ (A),AA ( fixed), is a probability charge satisfyingQ (N)=0, , for allP-zero setsN, if and only ifL 1(,P|) has a lifting, which exists for any sub--algebra ofA ifL 1(,A P) is separable. Separability ofL 1(,A,P) implies also the existence of a strongly semiregular versionQ (A),A, , ofP(A|), A , i.e., Q (A), (AA fixed), is -measurable andAQ (A),A ( fixed), is a probability charge. Furthermore,P can be written as P 1+(1–)P 2, 01, whereP 1 are probability measures onA such thatP 1(A|),AA, has a semiregular version vanishing for anyP-zero setN andP 2 is singular with respect to any probability measure onA of the type ofP 1. In the case 0<<1 the probability measuresP j ,j=1, 2, are uniquely determined. The decomposition can be carried over to the case, where the additional condition thatQ (N)=0 for all and anyP-zero setN is valid, is omitted respectively semiregularity is replaced by (i) strong semiregularity, or (ii) classical regularity. In the last mentioned case (ii) the decomposition is multiplicative.  相似文献   

10.
In this paper we classify all real convexity theories that contain the standard convexity theory c. For this purpose we consider three subcases: finitary; infinitary and (sc\c)Ø; infinitary and sc=c. In each of these subcases one encounters a phenomenon resembling bifurcation.This research was supported by the Deutsche Forschungsgemeinschaft.  相似文献   

11.
Summary New classes of sets called -closed sets and s-closed sets are introduced and studied. Also, we introduce and study -continuous functions and s-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces -T1/2 and -Ts.  相似文献   

12.
Let G be a group with a set of operators such that Z(G) is -admissible. Central -automorphisms occur in the Krull-Remak-Schmidt Theorem. We discuss the existence of a central -endomorphism of G that is not an automorphism.2000 Mathematics Subject Classification: 20E36  相似文献   

13.
Let be a linearly ordered set, A() be the group of all order automorphisms of , and L() be a normal subgroup of A() consisting of all automorphisms whose support is bounded above. We argue to show that, for every linearly ordered set such that: (1) A() is an o-2-transitive group, and (2) contains a countable unbounded sequence of elements, the simple group A()/L() has exactly two maximal and two minimal non-trivial (mutually inverse) partial orders, and that every partial order of A()/L() extends to a lattice one (Thm. 2.1). It is proved that every lattice-orderable group is isomorphically embeddable in a simple lattice fully orderable group (Thm. 2.2). We also state that some quotient groups of Dlab groups of the real line and unit interval are lattice fully orderable (Thms. 3.1 and 3.2).  相似文献   

14.
Let X be a Banach space with a countable unconditional basis (e.g., X=2), X open. We show that is pseudoconvex if and only if for each affine complex line L in X the sheaf cohomology group H 1 (,I) vanishes, where I is the ideal sheaf of all holomorphic functions on that vanish on L. We also give an example that the condition H q (,)=0 for all q1 unlike in finite dimensions does not imply the pseudoconvexity of . Lastly, we prove an interpolation result. Mathematics Subject Classification (2002): 32T05, 46G20.  相似文献   

15.
Extensions from H 1(P) into H 1() (where P ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.  相似文献   

16.
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains n N converge to a solution of the same problem on a domain where is the limit of n in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on N.  相似文献   

17.
Let be a closed rectifiable curve and a region in the complex plane. Suppose for each , R() represents multiplication by an nxn-matrix of rational functions and F() is a finite rank operator, both acting on the Hilbert space L 2 n (). Sufficient conditions are given for the integer valued function dim ker (R()+F()) to be continuous at all but finitely many points in . This result is applied to singular integral operators.This work was partially supported by the National Science Foundation.  相似文献   

18.
Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u h Z =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W 0 m, p (), 1<p<,Y=W 0 m. 2 (),Z=W 0 m. max (2,p) ()Wm, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].
  相似文献   

19.
We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H < H |h|, where H > 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal.  相似文献   

20.
Summary We study integral functionals of the formF(u, )= f(u)dx, defined foru C1(;R k), R n . The functionf is assumed to be polyconvex and to satisfy the inequalityf(A) c0¦(A)¦ for a suitable constant c0 > 0, where (A) is then-vector whose components are the determinants of all minors of thek×n matrixA. We prove thatF is lower semicontinuous onC 1(;R k) with respect to the strong topology ofL 1(;R k). Then we consider the relaxed functional , defined as the greatest lower semicontinuous functional onL 1(;R k ) which is less than or equal toF on C1(;R k). For everyu BV(;R k) we prove that (u,) f(u)dx+c0¦Dsu¦(), whereDu=u dx+Dsu is the Lebesgue decomposition of the Radon measureDu. Moreover, under suitable growth conditions onf, we show that (u,)= f(u)dx for everyu W1,p(;R k), withp min{n,k}. We prove also that the functional (u, ) can not be represented by an inte- gral for an arbitrary functionu BVloc(R n;R k). In fact, two examples show that, in general, the set function (u, ) is not subadditive whenu BVloc(R n;R k), even ifu W loc 1,p (R n;R k) for everyp < min{n,k}. Finally, we examine in detail the properties of the functionsu BV(;R k) such that (u, )= f(u)dx, particularly in the model casef(A)=¦(A)¦.  相似文献   

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