Simplexes of L-subdivisions of Euclidean spaces

It is shown that necessary and sufficient conditions for a basic simplex of a point lattice in Eⁿ space to be an L-simplex are equivalent to conditions imposed on the coefficients a_ij of the form _i,j=1 ⁿ a_ijx_ix_j– _i=1 ⁿ a_iix_i. namely, that it should assume positive values for all possible integer values of the variables x₁..., x_n (excluding the obvious n+1 cases when the form is equal to 0). These conditions are obtained for n 5.Translated from Matematicheskie Zametkij Vol. 10, No. 6, pp. 659–670, December, 1971.     

Composition operators from large weighted Hardy spaces into the Dirichlet space

Given a large weighted Hardy space we show there exists a composition operatorC with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College.     

Dualraum und Topologie der (lokal) langsam wachsenden Nullösungen hypoelliptischer Differentialoperatoren

In this paper a representation by functions of the dual space of the space of (locally) slowly growing nullsolutions C _p,* of a hypoelliptic PDO P (D) is given. The topology of C _p,* is identical with the topology induced by D D(ⁿ⁺¹)₆. This has various topological consequences, especially: The space of slowly growing solutions is a topological sequential dense subspace of the space of locally slowly growing solutions.     

On the Space of Sequences of p-Bounded Variation and Related Matrix Mappings

The difference sequence spaces (), c(), and c ₀() were studied by Kzmaz. The main purpose of the present paper is to introduce the space bv _p consisting of all sequences whose differences are in the space _p , and to fill up the gap in the existing literature. Moreover, it is proved that the space bv _p is the BK-space including the space _p . We also show that the spaces bv _p and _p are linearly isomorphic for 1 p . Furthermore, the basis and the -, -, and -duals of the space bv _p are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv _p : ), (bv : _p ), and (bv _p : ₁), and the characterizations of some other matrix classes are obtained by means of a suitable relation.     

Equivalent criterion of Haar and Franklin systems in symmetric spaces

In the present article it is proved that if the Haar and Franklin systems are equivalent in a separable symmetric space E, the following condition holds: 0<_EE<1, (1) where _E and _E are the Boyd indices of the space E. It is already known that if condition (1) is fulfilled, it follows that the Haar and Franklin systems are equivalent in the space E. Thereby, this estabishes that condition (1) is necessary and sufficient for the equivalence of the Haar and Franklin systems in E.In proving the assertion a number of interesting constructions involving Haar and Franklin polynomials are presented and upper and lower bounds on the Franklin functions applied.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 96–101, September, 1992.     

Kurven Auf Orientierbaren Flächen

Let T denote a closed oriented surface and let there be given a basis ₁,..., _n, ₁,..., _n of H₁ (T; ) with _i · _j = _i · _j = 0, _i · _j = _ij as intersection numbers. Then one can construct an ordinary imbedding of T in 3-dimensional euklidian space, such that the given basis is represented by the meridians and parallels of latitude of that imbedding. If there is a given imbedding of T into an euclidian space of dimension n5, then one has a factorisation through an ordinary imbedding into 3-dimensional space, such that the given basis is represented by the meridians and parallels of latitude of that ordinary imbedding. If in the case n=4 the imbedding of T can be factorised through 3-dimensional space one has a further invariant. Besides the skewsymmetric intersection form there is a quadratic form which must take its normal form on the given basis in order to represent this basis by meridians and parallels of latitude as above.     

Finsler structures of negative curvature in ⊄-linear fibre spaces

Let X be a reduced compact complex space and EX a -linear fibre space. Let P(E) be the associated projective variety over X and let L(E) be the canonical line bundle over P(E). Generalizing a result of Kobayashi, we prove that E carries a Finsler metric of negative curvature if and only if L(E)_redP(E)_red carries an Hermitian metric of negative curvature.     

On the number of relations in the cohomology of a fixed point set

If _p (respectively S¹) acts on a space, then under certain conditions the _p (respectively Q) cohomology of each component of of the fixed point set can be generated as an algebra by at most the same number of elements as the cohomology of the space itself. It is shown below that the ideal of relations among these generators is generated by at most the number of generators in the ideal of relations defining the cohomology of the original space.     

Transformation of Wiener measure under anticipative flows

Summary LetT()=+F() be a transformation from the Wiener space to itself with the range ofF() assumed to be in the Cameron-Martin space. The absolute continuity and the density function associated withT is considered;T is assumed to be embedded in or defined through a parameterizationT _t =+F _t () andF _t is assumed to be differentiable int. The paper deals first with the case where the range of thet-derivative ofF _t () is also in the Cameron-Martin space and new representations for the Radon-Nikodym derivative and the Carleman-Fredholm determinant are derived. The case where thet-derivative ofF _t is not in the Cameron-Martin space is considered next and results on the absolute continuity and the density function, under conditions which are considerably weaker than previously known conditions, are presented.The work of the second author was supported by the fund for promotion of research at the Technion     

Charakterisierung nüchterner Räume

The categorySob of sober spaces is a full isomorphismclosed reflective subcategory of the categoryT _o of T_o-spaces (and continuous maps).SobT _o is characterized by: (i) every universal morphism of the adjunction is aT _o-epic embedding, and (ii) everyT _o-epic embedding, whose domain is sober, is a homeomorphism.Sob is the epi-reflective hull of the Sierpinski space D inT _o. A subspace of a sober space is sober, iff it is b-closed. A space is sober, iff it is a b-closed subspace of a power of D.     

Double Complexes and Cohomological Hierarchy in a Space of Weakly Invariant Lagrangians of Mechanics

For a given configuration space M and a Lie algebra G acting on M, the space V _0.0 of weakly G-invariant Lagrangians, i.e., Lagrangians whose motion equations left-hand sides are G-invariant, is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex by the method of spectral sequences, we arrive at the hierarchy in the space V _0.0: The double filtration {V _s.}, s = 0, 1, 2, 3, 4, = 0, 1, and the homomorphisms on every space {V _s.} are constructed. These homomorphisms take values in the cohomologies of the algebra G and the configuration space M. Every space {V _s.} is the kernel of the corresponding homomorphism, while the space itself is defined by its physical properties.     

Compact sets in the spaceL p (O,T; B)

Summary A characterization of compact sets in L^p (0, T; B) is given, where 1P and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space L^p (0,T; B) from estimates with values in some spaces X, Y or B where XBY with compact imbedding XB. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {f_n} is bounded in L^q(0,T; B) and in L _loc ¹ (0, T; X) and if {f_n/t} is bounded in L _loc ¹ (0, T; Y) then {f_n} is relatively compact in L^p(0,T; B), p相似文献   

Quantum Poisson processes and dilations of dynamical semigroups

Summary The notion of a quantum Poisson process over a quantum measure space is introduced. This process is used to construct new quantum Markov processes on the matrix algebraM _n with stationary faithful state . If (, ) is the quantum measure space in question ( a von Neumann algebra and a faithful normal weight), then the semigroupe ^tL of transition operators on (M _n , ) has generator whereu is an arbitrary unitary element of the centraliser of (M _n ,).Supported by the Netherlands Organization for Scientific Research NWO     

On a family of topologies on the spaceL p

We study a family of topologies {_s}_{0 on the space lp, 0s} is the protective topology on l_p generated by the family of multipliers m_y:l_pl_s, m_y(x)=x · y, where y ranges over the space l_p and 1/p + 1/q=1/s. Here l_s is taken with its standard topology generated by the norm for s 1 or a pseudonorm if 0s}_{0sp is strictly increasing and that all the topologies s}, 0s are not locally convex when 0Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 194–198.     

A Note on Capacity and Hausdorff Measure in Homogeneous Spaces

ggt We consider analogoues of classical Riesz capacity C and Hausdorff measure H in a homogeneous space (X,d,µ) . We prove that, under mild regularity conditions on (X,d,µ), the usual relations between C and H hold. The key step in the proof is a version of the so called Frostman Lemma in a homogeneous space.     

Gram Matrix Analysis of Finite Distance Spaces in Constant Curvature

We develop the utility of Gram matrix machinery as a tool to treat the geometry of simplices in space forms. A formula relating the determinant of a normalized Gram matrix to the geometry of the simplex it represents is presented. We then apply the tools to leaf spaces, i.e. the set of degree 1 vertices of a metric tree. One main result is that for a given metric space X there exists a constant ₀ < 0, such that X embeds into all hyperbolic spaces of curvature less than ₀, if and only if X is a leaf space.     

Some existence theorems for the Dirichlet problem for quasilinear elliptic equations

Summary The purpose of this paper is to establish the existence of a solution of the Dirichlet problem for a quasilinear elliptic equation. We prove that the problem (1), (2) is solvable for all _j (j=1,...), where _j are eigenvalues of a linear elliptic operator that is associated with a given quasilinear elliptic operator by a limiting process. We also discuss this problem with a boundary data in L². This leads in a natural way to the Dirichlet problem in a weighted Sobolev space.     

Singular surfaces and the rigidity of ℙ3

In this paper we give two elementary proofs for the rigidity of the complex projective space ₃ with respect to global deformations.     

Scalarization of Tangential Regularity of Set-Valued Mappings

A set-valued mapping M from a topological vector space E into a normed vector space F is tangentially regular at a point in its graph g p h M if the Clarke tangent cone to g p h M at is equal to the Bouligand contingent cone to g p h M at . In this paper we characterize, in several cases, this tangential regularity as the directional regularity of the scalar function _M defined by _M (x, y) : = d(y, M(x)). The results allow us to express, in a useful formula, the subdifferential of _M in terms of the normal cone to the graph of M.