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1.
In the first part [1] of the paper the basic boundary value problems of the mathematical theory of elasticity for three-dimensional anisotropic bodies with cuts were formulated. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems were formulated in the Besov
and Bessel-potential (
p
s
) spaces. In the present part we give the proofs of the main results (Theorems 7 and 8) using the classical potential theory and the nonclassical theory of pseudodifferential equations on manifolds with a boundary. 相似文献
2.
G. Oniani 《Georgian Mathematical Journal》1996,3(1):81-96
The problem is posed and solved whether the conditionsf L(1+1n+
L)2(2) and
are equivalent for functionsf L(2) (whereM
2, denotes the strong maximal operator corresponding to the frame {OX
,OY
}).The results obtained represent a general solution of M. de Guzmán's problem that was previously studied by various authors. 相似文献
3.
The multidimensional Sparr interpolation method is implemented in the Besov spaces
and the Lizorkin--Triebel spaces
. It is shown that this results in Besov spaces of type
. An interpolation theorem for Besov spaces using weak conditions of the form
is formulated. 相似文献
4.
Marilyn Breen 《Journal of Geometry》1999,65(1-2):50-53
Let
be a finite family of compact sets in the plane, and letk be a fixed natural number. If every three (not necessarily distinct) members of
have a union which is simply connected and starshaped viak-paths, then
and
is starshaped viak-paths. Analogous results hold for paths of length at most , > 0, and for staircase paths, although not for staircasek-paths.Supported in part by NSF grant DMS-9504249 相似文献
5.
For the quadratic complex moment problem
, we obtain necessary and sufficient conditions for the existence of representing measures supported in the unit circleT or in the closed unit disk
. We explicitly construct all finitely atomic representing measures supported inT or
which have the fewest atoms possible. For the quadratic
-moment problem in which the moment matrixM(1) is positive and invertible, there exists an ellipse D such that the minimal (3-atomic) representing measures are supported in the complement of the interior region of . Finally, we apply these results to obtain information on the location of the zeros of certain cubic polynomials.Dedicated to the memory of Velaho D. Bowman-FialkowBoth authors were partially supported by research grants from the National Science Foundation. The second-named author was also partially supported by an award from the State of New York/UUP Professional Development and Quality of Working Life Committee. 相似文献
6.
Semi-commutators of Toeplitz operators on the Bergman space 总被引:3,自引:0,他引:3
Dechao Zheng 《Integral Equations and Operator Theory》1996,25(3):347-372
In this paper several necessary and sufficient conditions are obtained for the semi-commutator
of Toeplitz operators
andT
g
with bounded pluriharmonic symbols on the unit ball to be compact on the Bergman space. Using
-harmonic function theory on the unit ball we show that
with bounded pluriharmonic symbolsf andg is zero on the Bergman space of the unit ball or the Hardy space of the unit sphere if and only if eitherf org is holomorphic.The author was supported in part by the National Science Foundation. 相似文献
7.
Let X and Y be two Hilbert spaces, and
the space of bounded linear transformations from X into Y. Let {A
}
be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (1991). In this work we proceed further to characterize {A
n} by a positive measure and a number T of
-valued functions a
0, . . . ,a
T–1; in the spectral form
, where
and is an
-valued Borel set function on [0, 2) such that
相似文献
8.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform
on
More precisely, we prove that for all
and
then for all measurable function f on
the conditions
and
imply f = 0, if and only if
where
are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004 相似文献
9.
The solutions of the equation
in
, where
are investigated,
Bessel potentials of higher order are defined, and recurrence relations
between these solutions and these Bessel potentials are obtained. It is
also proved that these solutions and the solutions of
, under certain conditions, are identical.
Received: 6 November 2002 相似文献
10.
A class of bounded operators on Sobolev spaces 总被引:2,自引:0,他引:2
We describe a class of nonlinear operators which are bounded on the
Sobolev spaces
, for
and 1 < p <
. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on
, for
and 1 < p <
; this extends the result of J. Kinnunen [7], valid for s = 1.
Received: 5 December 2000 相似文献
11.
Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem
where
is a matrix-function with bounded variation components,
is a vector-function belonging to the Carathéodory class corresponding to
are continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation. 相似文献
12.
Let H1(
) be the usual Hardy space on
. We show that the couple (H1(
), L(
) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH1(
) +L(
) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H1(
) to L1(
) and also from L(
) to L(
); (ii) V(Nf)=f, V is similtaneously bounded from L1(
) to H1(
) and from L(
) to L(
) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (Lp(
), BMO (
)) for every 1
相似文献
13.
Harald Löwe 《Geometriae Dedicata》1995,58(1):45-51
We construct symmetric planes associated with an arbitrary locally compact connected nearfield
. If
is a proper nearfield, i.e.
{;;}, then the tangent translation plane of this symmetric plane is not classical. All previously known examples of symmetric planes have classical tangent translation planes.Herrn Professor Dr. H. Salzmann zum 65. Geburtstag gewidmet 相似文献
14.
Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in
and of the system
where
is uniformly distributed in [0, l]s. 相似文献
15.
Harald Luschgy 《Probability Theory and Related Fields》1992,93(1):39-66
Summary Let
(Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of
(P) relative to
(Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft 相似文献
16.
We present several partial results, variants, and
consistency results concerning the following (as yet unsolved)
conjecture. If X is a graph
on the ground set V with
then
X has an edge coloring
F with
colors such that if
V is decomposed into
parts then there is one
in which F assumes all
values.Due to some unfortunate misunderstandings, this
paper appeared much later than we expected.* Research partially supported by NSF grants
DMS-9704477 and DMS-0072560. Research partially supported by Hungarian National
Research Grant T 032455. 相似文献
17.
For a class of Serre fibratations
with a weak formal base X (or with a degenerated
-algebra structure on the integral cohomology H*(X)), obstructions are defined by means of spherical twisting cochains of . In particular, for a given section
on n-skeleton of X, the problem of avoiding the (n+1)th obstruction
to the existence of a section on X
n+1 reduces to solving a system of linear equations with respect to cohomology elements of the groups
Homotopy classification theorems for sections as well as for weak formal maps are given, too. 相似文献
18.
Vladimir I. Levenshtein 《Designs, Codes and Cryptography》1997,12(2):131-160
A system of (Boolean) functions in
variables is called randomized if the functions preserve the property of their variables to be independent and uniformly distributed random variables. Such a system is referred to as
-resilient if for any substitution of constants for any
variables, where 0 i t, the derived system of functions in
variables will be also randomized. We investigate the problem of finding the maximum number
of functions in
variables of which any
form a
-resilient system. This problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays. We extend some results of design and coding theory, in particular, a duality in bounding the optimal sizes of codes and designs, in order to obtain upper and lower bounds on
. In some cases, these bounds turn out to be very tight. In particular, for some infinite subsequences of integers
they allow us to prove that
,
,
,
,
. We also find a connection of the problem considered with the construction of unequal-error-protection codes and superimposed codes for multiple access in the Hamming channel. 相似文献
19.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
20.
We equip the category
of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In particular, a Leibniz algebra becomes a Lie object in
and the universal enveloping algebra functor UL from Leibniz algebras to associative algebras factors through the category of cocommutative Hopf algebras in
. This enables us to prove a Milnor-Moore type theorem for Leibniz algebras. 相似文献