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1.
In what follows, C is the space of -periodic continuous real-valued functions with uniform norm, is the first continuity modulus of a function with step h, H n is the set of trigonometric polynomials of order at most n, is the set of linear positive operators (i.e., of operators such that for every ), is the space of square-integrable functions on ,
It is proved that coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every does not exceed and, for , is equal to the minimum of the quadratic functional
over the unit sphere of . Then it is calculated that Bibliography: 19 titles.  相似文献   

2.
A class of centrally-symmetric convex 12-topes (12-hedrons) in is described such that for an arbitrary prescribed norm on each polyhedron in the class can be inscribed in (circumscribed about) the -ball via an affine transformation, and this can be done with large degree of freedom. Bibliography: 5 titles.  相似文献   

3.
4.
The paper deals with the problem of recovering the parameters (functions) and of the Maxwell dynamical system
(tan is the tangent component; is a solution) by the response operator ( is the normal). The parameters determine the velocity , the c-metric , and the time . It is shown that for any fixed , the operator determines and in uniquely. Bibliography: 15 titles.  相似文献   

5.
This paper considers the approximation of the Kantorovich–Shepard operators in spaces for . For the Kantorovich–Shepard operators are defined by (1.1). Then
where is a positive number depending only on and , and $$ \varepsilon_{n} =\cases{ n^{-1}, & if \ 2$$ " align="middle" border="0"> ; \cr\nosm n^{-1}\log n, & if \ ; \cr\nosm n^{1-\lambda}, & if \ . \cr} $$  相似文献   

6.
The Plücker embedding of the complex projective space in the Grassmannian of bivectors is used for proving several theorems on the relationship between the complex structure of and its Riemannian geometry. It is shown that the separation set of in the Plücker model is the face of for a certain calibration. Bibliography: 11 titles.  相似文献   

7.
The C *-algebra generated by the operators of pseudodifferential boundary value problems on a manifold with smooth closed disjoint edges and boundary is studied. The operators act in the space L 2( ) L 2( ). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra Bibliography: 12 titles.  相似文献   

8.
We study operators (not necessarily linear) defined on a quasi-Bahach space X and taking values in the space of real-valued Lebesgue-measurable functions. Factorization theorems for linear and superlinear operators with values in the space are proved with the help of the Lorentz sequence spaces . Sequences of functions belonging to fixed bounded sets in the spaces are characterized for and . The possibility of distinguishing weak type operators (bounded in the space ) from operators factorizable through is obtained in terms of sequences of independent random variables. A criterion under which an operator is symmetrically bounded in order in , is established. Some refinements of the above-mentioned results are obtained for translation shift-invariant sets and operators. Bibliography: 30 titles.  相似文献   

9.
This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])
for a solution to the Hamilton–Jacobi nonlinear partial differential equation
where the Cauchy data are now a function semicontinuous from below, is the usual norm in , , and is a positive evolution parameter. We proved that the Lax formula solves the Cauchy problem (2) at all points , fixed save for an exceptional set of points R of the F type, having zero Lebesgue measure. In addition, we formulate a similar Lax-type formula without proof for a solution to a new nonlinear equation of the Hamilton–Jacobi-type:
where is a diagonal positive-definite matrix, mentioned in Part I and having interesting applications in modern mathematical physics.  相似文献   

10.
A bi-Lipschitz continuous mapping of a space X is a bijection such that , where . We write if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by the set of all bi-Lipschitz mappings of X that are not isometry. Thus, if and blip . For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows: where Bibliography: 2 titles.  相似文献   

11.
Suppose that X is a Banach space, K denotes the set of real numbers R or the set of nonnegative real numbers R {+}, is a family of linear operators from X into X such that T 0=I is the identity operator in X, for all , and there exists M such that for all . The expression is called the rth order modulus of continuity of an element x with step h in the space X with respect to the family A(K). The properties of are studied. Bibliography: 3 titles.  相似文献   

12.
Let be a family of translations of a convex compact set such that every two elements of have a common point. Then there exist three points such that each element of contains one of these points. This answers in the affirmative an old question by Grünbaum. Bibliography: 13 titles.  相似文献   

13.
An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface with a prescribed set of distinguished points to the case of the Teichmüller space corresponding to under quasiconformal homeomorphisms f. For the functional of our problem on extremal decomposition of a surface , we consider a function expressing the dependence of the extremal value of on a point . Differentiation formulas for the function are derived. These formulas are different and depend on the genus g of the surface . The case where the function is pluriharmonic is considered. Bibliography: 8 titles.  相似文献   

14.
Let be a sequence of independent equidistributed random vectors with . Let , where and denotes the indicator function of the event in brackets. If, for example, are the gains and are the indicators of success in repetitions of a game of chance, then is the maximal gain along head runs (sequences of successes without interruptions) of length j. We investigate the asymptotic behavior of the values , , where is the length of the longest head run in . We show that the asymptotics of the values depend significantly on the growth rate of j and that these asymptotics vary from the strong noninvariance (as in the ErdsRéenyi law of large numbers) to the strong invariance (as in the CsöorgRévész strong approximation laws). We also consider the Shepp-type statistics. Bibliography: 17 titles.  相似文献   

15.
Let be an associative ring with identity, and let be the category of left unitary -modules. A complete characterization of continuous additive co- and contravariant functors is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to and, therefore, are equivalent to the category of compact right -modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right -modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles.  相似文献   

16.
Danilov  L. I. 《Mathematical Notes》2003,73(1-2):46-57
We prove the absolute continuity of the spectrum of the Schrödinger operator in , , with periodic (with a common period lattice ) scalar and vector potentials for which either , , or the Fourier series of the vector potential converges absolutely, , where is an elementary cell of the lattice , for , and for , and the value of is sufficiently small, where and otherwise, , and .  相似文献   

17.
The Markov-type inequality is proved for all polynomials of degree at most n with coefficients from {-1,0,1} with an absolute constant c. Here ·[0,1] denotes the supremum norm on [0,1]. The Bernstein-type inequality is shown for every polynomial p of the form The inequality is also proved for every analytic function p on the open unit disk D that satisfies the growth condition   相似文献   

18.
In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.  相似文献   

19.
Let be nonempty convex bodies in . Let be vectors in , let , and let . Then is a convex set, and the family of sets is concave. Let . Then for the mean cross-sectional measures W_v (\Phi (\rho )), , the functions are concave on D. (Note that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGxbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiabfA6agjaacIcacqaH% bpGCcaGGPaGaaiykaiabg2da9iaabAfacaqGVbGaaeiBamaaBaaale% aatCvAUfKttLearyqr1ngBPrgaiuGacqWFRbWAaeqaaOGaeuOPdyKa% aiikaiabeg8aYjaacMcaaaa!4EE7!\[W_0 (\Phi (\rho )) = {\text{Vol}}_k\Phi (\rho )\] is the k-volume.) Bibliography: 2 titles.  相似文献   

20.
This paper studies irreducible matrices , satisfying Brualdi's conditions , or, shortly, Brualdi matrices. Here, is the set of circuits of length in the directed graph of A, and is the support of . Among the results obtained are a characterization of Brualdi matrices, implying, in particular, that they are generalized diagonally dominant; the necessary and sufficient conditions of singularity of Brualdi matrices; explicit expressions for the absolute values of the components of right null-vectors of a singular Brualdi matrix, and conditions necessary and sufficient for a boundary point of Brualdi's inclusion region to be an eigenvalue of an irreducible matrix. Bibliography: 8 titles.  相似文献   

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