共查询到16条相似文献,搜索用时 15 毫秒
1.
The solutions of the Carathéodory–Fejér interpolation problem for generalized Schur functions can be parametrized via a linear fractional transformation over the class of classical Schur functions. The linear fractional transformation of some of these functions may have a pole (simple or multiple) in one or more of the interpolation points or not satisfy one or more interpolation conditions, hence not all Schur functions can serve as a parameter. The set of excluded parameters is characterized in terms of the related Pick matrix.Research was supported by the Summer Research Grant from the College of William and MarySubmitted: June 26, 2002 Revised: January 31, 2003 相似文献
2.
Grażyna Kwiecińska 《Mathematica Slovaca》2014,64(2):315-332
Let I ? ? be an interval and Y a reflexive Banach space. We introduce the (H) property of a multifunction F from I × Y to Y and prove that the Carathéodory superposition of F with each continuous function f from I to Y is a derivative provided that F has the (H) property. Some application of this theorem to the existence of solutions of differential inclusions f′(x) ∈ F(x, f(x)) is given. 相似文献
3.
We derive left and right quotient representations for central q × q matrix-valued Carathéodory functions. Moreover, we obtain recurrent formulas for the matrix polynomials involved in the quotient representations. These formulas are the starting point for getting recurrent formulas for those matrix polynomials which occur in the Arov-Krein resolvent matrix for the nondegenerate matricial Carathéodory problem. 相似文献
4.
Ricardo Uribe-Vargas 《Journal of Geometry》2003,77(1-2):184-192
We discuss three classes of closed curves in the Euclidean space $\mathbb{R}^{3}$ which have non-vanishing
curvature and at least 4 flattenings (points at which the torsion vanishes). Calling these classes (de.ned below)
Barner, Segre and Carathéodory, we prove that Barner $\subset$ (Segre $\cap$ Carathéodory). We also prove that (Segre)\
(Segre $\cap$ Carathéodory) and (Carathéodory)\(Segre $\cap$ Carathéodory) are open sets in the space of closed smooth
curves with the C-topology. Finally, we define a class of closed curves containing the class of Segre curves
and -based on contact topology considerations, as the Huygens principle- we establish the conjecture that any
curve of our class has at least 4 flattenings. 相似文献
5.
Maria Karmanova 《Geometric And Functional Analysis》2011,21(6):1358-1374
We develop a new approach to studying the geometry of Carnot–Carathéodory spaces under minimal assumptions on the smoothness
of basis vector fields. We obtain quantitative comparison estimates for the local geometries of two different local Carnot
groups, as well as of a local Carnot group and the original space. As corollaries, we deduce some results that are well-known
and basic for the “smooth” case: the generalized triangle inequality for d
∞, the local approximation theorem for the quasimetric d
∞, the Rashevskiǐ–Chow theorem, the ball-box theorem, and so on. 相似文献
6.
Bai Zhongzhi 《数学研究与评论》1998,(4)
1.IntroductionForapositivenumber1p∞andacomplexmatrixA=(aij)∈Cn×n,wedenoteby|A|p=ni,j=1|aij|p1pthelpnormofthematrixA,andbyA... 相似文献
7.
Prof. Dr Vlastimil Pták DrSc 《manuscripta mathematica》1988,62(2):131-144
In this paper we deal with singularities of the linear systems of plane curves passing through S, where S is a zerodimensional closed subscheme of degree n of
P
2=P
k
2
,k an algebraically closed field of any characteristic. We determine the least degree of a nonsingular curve passing through S, when S is in uniform position.
This paper was written while the author was member of C.N.R., Sez. 3 of G.N.S.A.G.A. and was supported by M.P.I. funds 相似文献
8.
The spaces dual to spaces of holomorphic functions of given growth on Carathéodory domains are described by using the Cauchy transform of functionals. A pseudoanalytic extension of such transforms to the whole plane is constructed, which makes it possible to remove convexity constrains and consider spaces determined by weights of general form, rather than only by those whose dependence on the distance from a point of the domain to its boundary is one-dimensional. 相似文献
9.
D. S. Lubinsky 《Constructive Approximation》2011,34(3):357-369
Let μ be a compactly supported positive measure on the real line, with associated Christoffel functions λ
n
(d
μ,⋅). Let g be a measurable function that is bounded above and below on supp[μ] by positive constants. We show that λ
n
(g
d
μ,⋅)/λ
n
(d
μ,⋅)→g in measure in {x:μ′(x)>0} and consequently in all L
p
norms, p<∞. The novelty is that there are no local or global restrictions on μ. The main idea is a new maximal function estimate for the “tail” in Nevai’s operators. 相似文献
10.
We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations. 相似文献
11.
Boundedness of Area Functions Related to Schrödinger Operators and Their Commutators in Weighted Hardy Spaces
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In this paper, we consider the area function $S_Q$ related to the Schrödinger operator $\mathcal{L}$ and its commutator $S_{Q,b}$, establish the boundedness of $S_Q$ from $H^p_\rho(w)$ to $L^p(w)$ or $WL^p(w),$ as well as the boundedness of $S_{Q,b}$ from $H^1_\rho(w)$ to $WL^1(w).$ 相似文献
12.
The paper is devoted to establishing a two-sided relation between the Darlington realizations of matrix functions from the Carathéodory class and their J p,r -inner SI-dilations. 相似文献
13.
Germund Dahlquist 《BIT Numerical Mathematics》1999,39(1):51-78
This is the last part of a work that has been divided into three parts. It contains Sections 4 and 5. Part I and Part II were published in BIT, vol. 37. Some amendments to the earlier parts are given in an appendix of this part.The reader is referred to Part I for the abstract, the contents and the references of the whole work. A short list of references for this part is found at the end of this part. A few new references of interest for the earlier parts are included. 相似文献
14.
15.
The Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability p≥1) on fractal d-sets is studied. Denoting by s∈(0,1] the smoothness parameter, the sharp upper bound min{d+1?s,d/s} is obtained. In particular, when passing from d≥s to d<s there is a change of behaviour from d+1?s to d/s which implies that even highly nonsmooth functions defined on cubes in ? n have not so rough graphs when restricted to, say, rarefied fractals. 相似文献
16.
M. I. Graev 《Acta Appl Math》2004,81(1):93-120
Complex analogs of the Gelfand–Tsetlin patterns are introduced. Infinite-dimensional representations of $\mathfrak{g}\mathfrak{l}\left( {n,\mathbb{C}} \right)$ in the vector spaces spanned on these patterns are constructed. Exponentials of these representations are described. These exponentials are operators T(x), x∈GL(n,C), defined only in neighborhoods of the identity element of GL(n,C). A system of differential-difference equations for matrix elements of operators T(x) is constructed. Explicit formulas for matrix elements are obtained for the case x∈Z ±, where Z + and Z ? are the triangular unipotent subgroups. Representations of $\mathfrak{g}\mathfrak{l}\left( {n,\mathbb{C}} \right)$ are also constructed; bases of these representations consist of Gelfand–Tsetlin patterns having infinitely many rows. 相似文献