共查询到20条相似文献,搜索用时 31 毫秒
1.
M. C. Zdun 《Aequationes Mathematicae》2001,61(3):239-254
Summary. We investigate the bounded solutions j:[0,1]? X \varphi:[0,1]\to X of the system of functional equations¶¶j(fk(x))=Fk(j(x)), k=0,?,n-1,x ? [0,1] \varphi(f_k(x))=F_k(\varphi(x)),\;\;k=0,\ldots,n-1,x\in[0,1] ,(*)¶where X is a complete metric space, f0,?,fn-1:[0,1]?[0,1] f_0,\ldots,f_{n-1}:[0,1]\to[0,1] and F0,...,Fn-1:X? X F_0,...,F_{n-1}:X\to X are continuous functions fulfilling the boundary conditions f0(0) = 0, fn-1(1) = 1, fk+1(0) = fk(1), F0(a) = a,Fn-1(b) = b,Fk+1(a) = Fk(b), k = 0,?,n-2 f_{0}(0) = 0, f_{n-1}(1) = 1, f_{k+1}(0) = f_{k}(1), F_{0}(a) = a,F_{n-1}(b) = b,F_{k+1}(a) = F_{k}(b),\,k = 0,\ldots,n-2 , for some a,b ? X a,b\in X . We give assumptions on the functions fk and Fk which imply the existence, uniqueness and continuity of bounded solutions of the system (*). In the case X = \Bbb C X= \Bbb C we consider some particular systems (*) of which the solutions determine some peculiar curves generating some fractals. If X is a closed interval we give a collection of conditions which imply respectively the existence of homeomorphic solutions, singular solutions and a.e. nondifferentiable solutions of (*). 相似文献
2.
Esa Järvenpää Maarit Järvenpää Antti Käenmäki Tapio Rajala Sari Rogovin Ville Suomala 《Mathematische Zeitschrift》2010,266(1):83-105
Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dimp(A) £ s-crs{{\rm {dim}_p}(A)\le s-c\varrho^s} where dimp is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the
corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that
dimp(A) £ dimp(X)-c(log\tfrac1r)-1rt{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} . 相似文献
3.
S. B. Damelin F. J. Hickernell D. L. Ragozin X. Zeng 《Journal of Fourier Analysis and Applications》2010,16(6):813-839
Given $\mathcal{X}Given X\mathcal{X}, some measurable subset of Euclidean space, one sometimes wants to construct a finite set of points, P ì X\mathcal{P}\subset\mathcal {X}, called a design, with a small energy or discrepancy. Here it is shown that these two measures of design quality are equivalent
when they are defined via positive definite kernels
K:X2(=X×X)?\mathbbRK:\mathcal{X}^{2}(=\mathcal{X}\times\mathcal {X})\to\mathbb{R}. The error of approximating the integral òXf(x) dm(x)\int_{\mathcal{X}}f(\boldsymbol{x})\,\mathrm{d}\mu(\boldsymbol{x}) by the sample average of f over P\mathcal{P} has a tight upper bound in terms of the energy or discrepancy of P\mathcal{P}. The tightness of this error bound follows by requiring f to lie in the Hilbert space with reproducing kernel K. The theory presented here provides an interpretation of the best design for numerical integration as one with minimum energy,
provided that the measure μ defining the integration problem is the equilibrium measure or charge distribution corresponding to the energy kernel, K. 相似文献
4.
S. Reifferscheid 《Archiv der Mathematik》2000,75(3):164-172
Let \frak X, \frak F,\frak X\subseteqq \frak F\frak {X}, \frak {F},\frak {X}\subseteqq \frak {F}, be non-trivial Fitting classes of finite soluble groups such that G\frak XG_{\frak {X}} is an \frak X\frak {X}-injector of G for all G ? \frak FG\in \frak {F}. Then \frak X\frak {X} is called \frak F\frak {F}-normal. If \frak F=\frak Sp\frak {F}=\frak {S}_{\pi }, it is known that (1) \frak X\frak {X} is \frak F\frak {F}-normal precisely when \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and consequently (2) \frak F í \frak X\frak N\frak {F}\subseteq \frak {X}\frak {N} implies \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and (3) there is a unique smallest \frak F\frak {F}-normal Fitting class. These assertions are not true in general. We show that there are Fitting classes \frak F\not = \frak Sp\frak {F}\not =\frak {S}_{\pi } filling property (1), whence the classes \frak Sp\frak {S}_{\pi } are not characterized by satisfying (1). Furthermore we prove that (2) holds true for all Fitting classes \frak F\frak {F} satisfying a certain extension property with respect to wreath products although there could be an \frak F\frak {F}-normal Fitting class outside the Lockett section of \frak F\frak {F}. Lastly, we show that for the important cases \frak F=\frak Nn, n\geqq 2\frak {F}=\frak {N}^{n},\ n\geqq 2, and \frak F=\frak Sp1?\frak Spr, pi \frak {F}=\frak {S}_{p_{1}}\cdots \frak {S}_{p_{r}},\ p_{i} primes, there is a unique smallest \frak F\frak {F}-normal Fitting class, which we describe explicitly. 相似文献
5.
Relative Artin motives and the reductive Borel–Serre compactification of a locally symmetric variety
We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we consider the universal Artin motive mapping to M and denote it w0X(M)\omega^{0}_{X}(M). We use this to define a motive
\mathbbEX\mathbb{E}_{X} over X which is an invariant of the singularities of X. The first half of the paper is devoted to the study of the functors w0X\omega^{0}_{X} and the computation of the motives
\mathbbEX\mathbb{E}_{X}. 相似文献
6.
We extend a result of ?estakov to compare the complex interpolation method [X 0, X 1]θ with Calderón-Lozanovskii’s construction ${{{{X^{1-\theta}_{0}X^{\theta}_{1}}}}}We extend a result of Šestakov to compare the complex interpolation method [X
0, X
1]θ with Calderón-Lozanovskii’s construction X1-q0Xq1{{{{X^{1-\theta}_{0}X^{\theta}_{1}}}}}, in the context of abstract Banach lattices. This allows us to prove that an operator between Banach lattices T : E → F which is p-convex and q-concave, factors, for any q ? (0, 1){{{{\theta \in (0, 1)}}}}, as T = T
2
T
1, where T
2 is (
(\fracpq+ (1 - q)p ){{\left({\frac{p}{{\theta + (1 - \theta)p}}} \right)}}-convex and T
1 is
(\fracq1 - q ){{\left({\frac{q}{{1 - \theta }}} \right)}}-concave. 相似文献
7.
Jun Wu 《Monatshefte für Mathematik》2006,54(4):259-264
For
log\frac1+?52 £ l* £ l* < ¥{\rm log}\frac{1+\sqrt{5}}{2}\leq \lambda_\ast \leq \lambda^\ast < \infty
, let E(λ*, λ*) be the set
{x ? [0,1): liminfn ? ¥\fraclogqn(x)n=l*, limsupn ? ¥\fraclogqn(x)n=l*}. \left\{x\in [0,1):\ \mathop{\lim\inf}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda_{\ast}, \mathop{\lim\sup}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda^{\ast}\right\}.
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
dimE(l*, l*) 3 \fracl* -log\frac1+?522l*\dim E(\lambda_{\ast}, \lambda^{\ast}) \ge \frac{\lambda_{\ast} -\log \frac{1+\sqrt{5}}{2}}{2\lambda^{\ast}} 相似文献
8.
Shahar Mendelson 《Geometric And Functional Analysis》2010,20(4):988-1027
We study the empirical process ${{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}We study the empirical process
supf ? F|N-1?i=1N f2(Xi)-\mathbbEf2|{{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}, where F is a class of mean-zero functions on a probability space (Ω, μ), and (Xi)i = 1N{(X_{i})_{i =1}^N} are selected independently according to μ. 相似文献
9.
Atsushi Shiho 《Selecta Mathematica, New Series》2011,17(4):833-854
Let
X \hookrightarrow[`(X)]{X \hookrightarrow \overline{X}} be an open immersion of smooth varieties over a field of characteristic p > 0 such that the complement is a simple normal crossing divisor and [`(Z)] í Z í [`(X)]{\overline{Z}\subseteq Z \subseteq \overline{X}} closed subschemes of codimension at least 2. In this paper, we prove that the canonical restriction functor between the categories
of overconvergent F-isocrystals F-Isocf(X,[`(X)]) ? F-Isocf(X\Z,[`(X)]\[`(Z)]){F-{\rm Isoc}^\dagger(X,\overline{X}) \longrightarrow F-{\rm Isoc}^\dagger(X{\setminus}Z, \overline{X}{\setminus}\overline{Z})} is an equivalence of categories. We also give an application of our result to the equivalence of certain categories. 相似文献
10.
Green’s relations and regularity for semigroups of transformations that preserve double direction equivalence 总被引:1,自引:0,他引:1
Let T X denote the full transformation semigroup on a set X. For an equivalence E on X, let $T_{E^*}(X)=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E\Leftrightarrow(x\alpha,y\alpha)\in E\}.$ Then $T_{E^{*}}(X)Let T
X
denote the full transformation semigroup on a set X. For an equivalence E on X, let
TE*(X)={a ? TX:"x,y ? X,(x,y) ? E?(xa,ya) ? E}.T_{E^*}(X)=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E\Leftrightarrow(x\alpha,y\alpha)\in E\}. 相似文献
11.
For a resistance form ${(X, \mathcal{D}(\varepsilon),\varepsilon)}
12.
Masato Kikuchi 《Mathematische Zeitschrift》2010,265(4):865-887
Let ${\Phi : \mathbb{R} \to [0, \infty)}
13.
Let ${\mathbb {F}}
14.
The bigraded Frobenius characteristic of the Garsia-Haiman module M
μ
is known [7, 10] to be given by the modified Macdonald polynomial [(H)\tilde]m[X; q, t]{\tilde{H}_{\mu}[X; q, t]}. It follows from this that, for
m\vdash n{\mu \vdash n} the symmetric polynomial ?p1 [(H)\tilde]m[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t]} is the bigraded Frobenius characteristic of the restriction of M
μ
from S
n
to S
n-1. The theory of Macdonald polynomials gives explicit formulas for the coefficients c
μ
v
occurring in the expansion ?p1 [(H)\tilde]m[X; q, t] = ?v ? mcmv [(H)\tilde]v[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t] = \sum_{v \to \mu}c_{\mu v} \tilde{H}_{v}[X; q, t]}. In particular, it follows from this formula that the bigraded Hilbert series F
μ (q, t) of M
μ
may be calculated from the recursion Fm (q, t) = ?v ? mcmv Fv (q, t){F_\mu (q, t) = \sum_{v \to \mu}c_{\mu v} F_v (q, t)}. One of the frustrating problems of the theory of Macdonald polynomials has been to derive from this recursion that Fm(q, t) ? N[q, t]{F\mu (q, t) \in \mathbf{N}[q, t]}. This difficulty arises from the fact that the c
μ
v
have rather intricate expressions as rational functions in q, t. We give here a new recursion, from which a new combinatorial formula for F
μ
(q, t) can be derived when μ is a two-column partition. The proof suggests a method for deriving an analogous formula in the general case. The method
was successfully carried out for the hook case by Yoo in [15]. 相似文献
15.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
|