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1.
We prove that if (,D) is a positivity preserving form on L 2 (E;m), and if (u n)n is a sequence in D() converging m-almost everywhere to u L 2 (E;m), then (u,u) lim infn (u n ,u n ).  相似文献   

2.
In the present note a theorem about strong suitability of the space of algebraic polynomials of degree n in C[a,b] (Theorem A in [1]) is generalized to the space of spline polynomials [a, b ]n, k (n2, 0) in C[a, b]. Namely, it is shown that the following theorem is valid: for arbitrary numbers 0, 1, ..., n+k, satisfying the conditions (ii–1) (i+1{ i< 0(i=1, ..., n +k–1), there is a unique polynomials n,k (t) [a, b ]/n,k and pointsa=0,<1<...< n+k– 1< n+k = b (11 <n, ..., kk<n+k–1), such that sn,k(i) = i(i=0, ..., n + k), sn,k(i)=0 (i=1, ..., n + k–1).Translated from Matematicheskii Zametki, Vol. 11, No. 3, pp. 251–258, March, 1972.  相似文献   

3.
The lowest upper bound is obtained for best one-sided approximations of classes (r=1,2 ...) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space L, where WrL={f:f(x+2)=f(x), f(r–1)(x) is absolutely continuous, f (r)L 1} and L is an Orlicz space.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 257–267, August, 1977.  相似文献   

4.
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   

5.
Anders [1] showed, that the remainder term ofn-dimensional Romberg integrationT m,k is of orderO(4km ) fork . Here, by induction overn and the results [2] forn = 1, an explicit formula is derived, giving the precise constants. It follows, that forf continuous andm +k theT m,k are converging to the value of the integral.  相似文献   

6.
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   

7.
We prove the existence of bounded solutions for a class of nonlinear elliptic problems of type–div(a(x,u,Du))=H(x,u,Du)+f, uW 1,p 0()L (),where a(x,,)b(||)|| p , b is a continuous monotone decreasing function and |H(x,,)| k()|| p , k is a continuous monotone increasing function.  相似文献   

8.
If is a complex, separable Hilbert space, letL 2 () denote theL 2-space of functions defined on the unit circle and having values in . The bilateral shift onL 2() is the operator (U f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapHK is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL 2(), that are carried into themselves contractively byU . We also do this for the subcase of those spaces which are carried into themselves unitarily byU .  相似文献   

9.
Summary Fix a curve X of genus g and L Pic d (X). Let L(X) be the image of X through the complete linear system H0(X, L). Here we prove that a general projection of L(X) intoP N has maximal rank if either (a) N4, 0gN–1, dg+N, or (b) dd (g, N) for suitable d(g, N).  相似文献   

10.
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   

11.
Zusammenfassung Die zeitabhängige (instationäre) Lösung für die Zustandswahrscheinlichkeiten und für einige Kenngrößen von Warteschlangensystemen mit einer Bedienungsstation, unendlich vielen Warteplätzen, exponentiellem Zu- und Abgang und beliebigem Anfangszustand wird bestimmt. Die ZustandswahrscheinlichkeitenP v (), d. h. die Wahrscheinlichkeiten für Einheiten im System zur Zeit, ergeben sich als Integrale, in denen modifizierteSessel-Funktionen 1. Art auftreten. Der ErwartungswertL () und die VarianzV() der Zahl von Einheiten im System lassen sich als Integrale darstellen, in denen nur die ZustandswahrscheinlichkeitP 0() auftritt.Für<1 und erreichen die Systeme einen stationären Zustand (für den die Lösung bekannt ist); für1 und giltP v ()0 für alle, L(),V().Ist>1, dann wachsenL() undV() für große linear mit; ihre Asymptoten werden berechnet. Ist=1, dann wachsenL() und die Standardabweichung() für große mit ; einfache Näherungsformeln werden gefunden.
Summary The time dependent solution is determined for the state probabilities and for some characteristic values of queuing systems with a single server, an infinite number of waiting places, exponentially distributed inter-arrival and service times, and any initial state. The state probabilitiesP v (), i.e. the probabilities for units in the system at time, are given in the form of integrals in which modifiedBessel functions of the first kind occur. Integrating the state probalityP 0() over leads to the meanL() and the varianceV() of the number of units in the system.For<1 and the systems tend to a steady state (for which the solution is known); for1 and we haveP v ()0 for all, L(),V().If>1 asymptotic expansions for large are found givingL() andV() proportional to. If=1 simple approximate formulas for large are obtained givingL() and the standard deviation() proportional to .


Vorgel. v.:J. Nitsche.  相似文献   

12.
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   

13.
We consider the abstract dynamical framework of [LT3, class (H.2)] which models a variety of mixed partial differential equation (PDE) problems in a smooth bounded domain n , arbitraryn, with boundaryL 2-control functions. We then set and solve a min-max game theory problem in terms of an algebraic Riccati operator, to express the optimal quantities in pointwise feedback form. The theory obtained is sharp. It requires the usual Finite Cost Condition and Detectability Condition, the first for existence of the Riccati operator, the second for its uniqueness and for exponential decay of the optimal trajectory. It produces an intrinsically defined sharp value of the parameter, here called c (critical), c0, such that a complete theory is available for > c, while the maximization problem does not have a finite solution if 0 < < c. Mixed PDE problems, all on arbitrary dimensions, except where noted, where all the assumptions are satisfied, and to which, therefore, the theory is automatically applicable include: second-order hyperbolic equations with Dirichlet control, as well as with Neumann control, the latter in the one-dimensional case; Euler-Bernoulli and Kirchhoff equations under a variety of boundary controls involving boundary operators of order zero, one, and two; Schroedinger equations with Dirichlet control; first-order hyperbolic systems, etc., all on explicitly defined (optimal) spaces [LT3, Section 7]. Solution of the min-max problem implies solution of theH -robust stabilization problem with partial observation.The research of C. McMillan was partially supported by an IBM Graduate Student Fellowship and that of R. Triggiani was partially supported by the National Science Foundation under Grant NSF-DMS-8902811-01 and by the Air Force Office of Scientific Research under Grant AFOSR-87-0321.  相似文献   

14.
We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S | in the spaceL 2(, ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union =12 of two simple piecewise Lyapunov curves we prove that the essential norm |S | inL 2() is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S | in the spaceL 2() as well as inL 2(, ) does not depend on the values of the angles and it can be calculated by formula (5).  相似文献   

15.
16.
In the case of certain geometries () [1] over kinematic algebras [5],[6] the -trace of the system of chains can be characterized by constant curvature. The curvature allows an affine interpretation of non-affine points.  相似文献   

17.
Let (–1,1), let 2/(1–)p<, letp denote the Hölder conjugate ofp, and let be an open arc of the unit circle. It is shown that, iff is a holomorphic function on the unit disc such that: (i) (1–|z|)log+|f(z)| isL p -integrable on the sector {r:0f has an infinite asymptotic value has -finite (2–(1+)p)-dimensional Hausdorff, measure, thenf has finite angular limits on a subset of of positive linear measure. In fact, a stronger conclusion will be established.  相似文献   

18.
LetG n ()be the semi-direct product of the symmetric groupS n by the Steinberg groupSt n ()of a ringWe first prove thatG n ()has a Coxeter-type presentation. The canonical morphism St n () GL n ()extends to a group homo Gn() GL n ()We next determine the kernel of for n = We also give an expression for the generator of the algebraic K group K 2(Z)of the integers in terms of permutation matrices.  相似文献   

19.
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   

20.
For X(t) a real-valued symmetric Lévy process, its characteristic function is E(e iX(t))=exp(–t()). Assume that is regularly varying at infinity with index 1<2. Let L x t denote the local time of X(t) and L* t =sup xR L x t . Estimates are obtained for P(L 0 t y) and P(L* t y) as y and t fixed.  相似文献   

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