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71.
We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of .
Received: 2 October 1996 / Revised version: 22 May 1997 相似文献
72.
Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic
inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results
on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number
of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient,
we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of
the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing
collisions between particles, which leads to a second-order limiting PDE.
Received: 5 August 1996 / In revised form: 17 October 1996 相似文献
73.
J. Schropp 《Numerische Mathematik》1997,78(1):87-101
Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent,
strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of
the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the
case of -stable formulae this leads to an efficient solver for stiff minimization problems.
Received July 10, 1995 / Revised version received June 27, 1996 相似文献
74.
Dorina Mitrea Marius Mitrea Jill Pipher 《Journal of Fourier Analysis and Applications》1997,3(2):131-192
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems
of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding
theory for Lp-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering. 相似文献
75.
Genkai Zhang 《manuscripta mathematica》1998,97(3):371-388
Let X=G
* be a compact Hermitian symmetric space. We study the Berezin transform on L
2(X) and calculate its spectrum under the decomposition of L
2(X) into the irreducible representations of G
*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical
line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X.
Received: 10 September 1996 / Revised version: 10 September 1997 相似文献
76.
The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions.
In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation
solutions.
Accepted 27 February 1996 相似文献
77.
H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
78.
Regularity of multiwavelets 总被引:7,自引:0,他引:7
The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields. 相似文献
79.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
80.
Kehe Zhu 《Integral Equations and Operator Theory》1998,31(3):371-387
The paper deals with two closely related questions about the Bergman space of the unit disk. First, we investigate a special class of invariant subspaces of the Bergman space, namely, invariant subspaces induced by certain Hankel operators. We show that such spaces always have the co-dimension 1 or 2 property; and we determine exactly when such a space has the co-dimension 1 property. Second, we introduce the notion of inner spaces in the Bergman space and give several characterizations of when an inner space is maximal.Research supported by the National Science Foundation 相似文献