共查询到20条相似文献,搜索用时 171 毫秒
1.
YANG Dachun Department of Mathematics Beijing Normal University Beijing China 《中国科学A辑(英文版)》2005,48(1):12-39
Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|<(?) andmax{d/(d+(?)),d/(d+s+(?))}<q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p≤∞ and 0<q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p<∞ and max{d/(d+(?)),d/(d+s+(?))}<q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s=0 and q=2,thenH(?)_∞q~s(X)=(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)=BMO(X). 相似文献
2.
BU Shangquan 《数学年刊B辑(英文版)》2001,22(4):513-518
Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W… 相似文献
3.
<正> §1.问题与结果考虑非线性方程(E) y″+f(x,y)=0.当 f 满足条件(H) f∈C{a≤x≤b;|y|<∞},且当 y(?)0时 y·f>0时,我们称方程(E)为(E)型方程.Atkinson [1]、Nehari [2]、Moroney [3]、Pimbley [4]等人曾经认为(或默认为),(E)型方程的任一解都能开拓到整个区间[a,b].我们曾在文[5]中指出,这个问题值得讨论.接着本文初稿和[6]构造了反例,阐明此结论不成立;同时研究了(E)型方程任一解都能开拓到 b 的充分条件.所得部份结果如下: 相似文献
4.
Yan Shaozong 《数学年刊B辑(英文版)》1980,1(34):485-499
Let H be a Hilbert space, and let A be a linear bounded operator on H. For
\(\lambda \in \rho (A)\), the \({U_\lambda } = {(A - \lambda )^{ * - 1}}(A - \lambda )\) is called polar.Produot operator.
In this paper, we discuss the properties of \({U_\lambda }\) and the relation between \({U_\lambda }\) and A. We obtain tbe following results.
Definition. Let B be a linear bounded operator on H, suppose \(0 \in \rho (B)\). For every
\(x,y \in H\), we definite \([x,y] = (Bx,y)(H,B)\)(or (H, [·,·]) is called a non-
degenerate bilinear space (it is obvious that if B=B*,then (H,B)is a space with an
indefinite metric; and that if B>0, then (H,B) is a Hilbert Space. If an operator
U(A) satisfies
\[[Ux,Uy] = [x,y]([Ax,y] = [x,Ay]),x,y \in H\]
then the operator U(A) is called a wvitary (self adjoint) on (H,B).
Theorem I . Suppose A is a linear bounded operator on H,
(1) If \(0 \in \rho (A)\), then \(U = {A^{ * - 1}}A\) is a unitary operator on (H,A) or (H, A*), and \(\sigma (U) = \frac{1}{{\sigma (U)}}\).
(2) If there is a complex number \(\alpha \), such that \({\mathop{\rm Im}\nolimits} A \ge \alpha > 0\) then a)\(0 \in \rho (A)\), and
the operator \(U = {A^{ * - 1}}A\) is a unitary on Hilbert space \((H,{\mathop{\rm Im}\nolimits} A) and 1 \in \rho (U)\);b) there exist two Hilbert spaces \((H,{v_1}),(H,{v_2})\), such that A, A* are all the unitary operator
from (H,v1) onto (H,v2), and there are two spectral measures \(\{ E_\lambda ^i,\lambda \in [\alpha ,\chi ] \subset (0,2\pi )\} ,i = 1,2,\), such that \(AE_\Delta ^1H \subset E_\Delta ^2H,{A^ * }E_\Delta ^1H \subset E_\Delta ^2H\) for any \(\Delta = (\lambda ,u] \subset (0,2\pi ]\).
(3) If \(0 \in \rho (A) \cap \rho ({\mathop{\rm Im}\nolimits} A)\) then the operator \(U = {A^{ * - 1}}A\) is a unitary on \((H,{\mathop{\rm Im}\nolimits} A)\).
with an indefinite met He, and \(1 \in \rho (U)\).
(4) For any complex number \(\lambda = r{e^{i\theta }},\left| \lambda \right| > \left\| A \right\|\), then \({U_\lambda }\) must be a unitary operator on the Hilbert space \(\left( {H,{\mathop{\rm Im}\nolimits} (\frac{1}{{i\lambda }}A + iI)} \right),and - {e^{i2\theta }} \in \rho ({U_\lambda })\)
Theorem 2. (1) A is a normal operator iff there exists a complex number \(\lambda \),
\(\lambda \in \rho (A)\), such that \(\frac{{\partial {U_\lambda }}}{{\partial \lambda }}{U_\lambda } = {U_\lambda }\frac{{\partial {U_\lambda }}}{{\partial \lambda }}\),where \(\frac{\partial }{{\partial \lambda }}\) is the directional derivative.
(2) If there exists a complex number \(\alpha ,{\mathop{\rm Im}\nolimits} A \ge \alpha > 0\) then A is a normal operator
iff \(U = {A^{ * - 1}}A\) is also.
(3) If A is a hyperiwrmal or a subnormal, then for every \(\lambda \in \rho (A),\sigma ({U_\lambda })\) lies on the circle.
3, 4期
关于极?积算子炉一U
499
Theorem 3? Let A be a linear bounded operator on Hm Suppose 0£p(J.)?
(1) If U=А*~гА is a unitary operator in a certain non-degenerate bilinear space
(H} 1 J |Л|>1 入 J Ш=1
solmble iff (l)cr(ü) =-=i=-, (2) the operotor Ui= f XdE\ is unitarity equivalent to
cr(C7) J |л|>1
the operator ül_1 == ШЕ1, 、
J 1Л|>1
If the conditions (1),(2) are satified, then we have
(3) the subspace JJi?^2 of H reduces any solution of the equation A*"1 A — U, and
1
AI (Ягея*)1 = ^Uo where Ъ is any in vertible self-adjoint on (i?i?J?2) L, and bv Uo
(Uo = Jiai i ЫЕ1 )}⑷41Я1фя, = , Ла = A1ü2, if the operator V is to
realize TJt and Ut^unitary equivalence^ then Ai = VSf where S is any invertible on Нг
and SvUi. "
Corollary. Swpp)se operator U is a normal on a certain Hilbert space(Hy v) (^the
U is similar to a certain normal operator on IT), if U satisfies the conditions (1)、(2) of
Theorem^ on ?S,v) ? Then the general form of the solution of А*~гА = U is A = vA'y
where A' is same as A in Theorem^.
Theorem 5. Let U be a linear bounded operator on H. Suppose O?p(J.)and p(ü)
is a simply connected region, then the equation А*~гЛ = U is a solvable iff there
exists a certain space {H,v) with a indefinite metric, such that U is a unitary operator
on (Hf 丨).
If is a unitary operator on ?H,v),then there exists a particular solution of
I X+$
А*~гА = U: Ar = 2e v [ (?7 —X)_1+X], where eie ? p (JJ), and the general form of the
solution is Аж АУ, wliere V is any in vertible self-adjoint on (H, -u)and VvU, 相似文献
5.
Bers型空间和复合算子 总被引:6,自引:0,他引:6
For α∈(0,∞),let Hα^∞(or Hα^∞,0)denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|^2)^α=O(1)(or|f(z)|(1-|z|^2)^α=o(1) as |z|→1).Hα^∞,0)is called a Bers-type space (or a little Bers-type space).In this paper,we give some basic properties of Hα^∞,Cψ,the composition operator associated with a symbol function ψ which is an analytic self map of D,is difined by Cψf=f o ψ,We characterize the boundedness,and compactness of Cψ which sends one Bers-type space to another function space. 相似文献
6.
<正> Throughout the present paper it is assumed that E is a real,locally convex,Hausdorfftopological vector space,and X(?)E a nonempty compact convex subset.A multi-valuedmapping F:X→2~E is said to be upper(lower) semicontinuous if for any open(closed) setU(?)E the set{x∈X|F(x)(?)U)is open (closed) in X;or,equivalently,for any closed(open) set V(?)E the set{X∈X|F(x)∩ V(?)(?)}is closed (open) in X.Moreover,F 相似文献
7.
Vesselin Vatchev 《分析论及其应用》2011,27(2):187-200
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed. 相似文献
8.
Xiang Yu ZHOU Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing P.R.China Department of Mathematics Zhejiang University Hangzhou P.R.China Wei Ming LIU Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing P.R.China 《应用数学学报(英文版)》2004,(4)
Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vectorbundle of rank r with trivial pull-back to W=C~n-{0}.We prove the existence of a non-vanishingsection of L(?)E for some line bundle on X and study the vector bundles filtration structure of E.These generalize the results of D.Mall about structure theorem of such a vector bundle E. 相似文献
9.
杨力华 《数学年刊B辑(英文版)》1991,(2)
The author gives some disagreement to the following result,which is published in [1].Let {L_n(f(}be mass-concerntative,φ_n→0+(n→∞),0<α≤2 andC~(-1)≤(φn+1)/(φn)≤C(n=1,2,…)for some constrant C>0.Then for any f∈C[-2a,2a],||L_n(f)-f||σ[-a,a]=O(φ_n~α)implies f∈Lip*α,whereLip*a={f∈C[-2a,2a]|w_2(f,δ)[-2a,2a]=O(δ~α)}.Then some similar results on C_(2π)are given,and further some results on C[-2a,2a]areestablished by adding some proper conditions. 相似文献
10.
林诒勋 《高校应用数学学报(英文版)》2003,18(3):361-369
§ 1 IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th… 相似文献
11.
A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS 总被引:2,自引:0,他引:2
Zhang Quande 《数学年刊B辑(英文版)》1995,16(4):461-468
ANECESSARYANDSUFFICIENTCONDITIONOFEXISTENCEOFGLOBALSOLUTIONSFORSOMENONLINEARHYPERBOLICEQUATIONS¥ZHANGQUANDE(DepartmentofMathe... 相似文献
12.
《复变函数与椭圆型方程》2012,57(7):553-563
Let D denote the open unit disk and $ f:D \to \bar {{\bf C}}$ be meromorphic and injective in D . Especially, we consider such f which have an expansion $$ f(z) = z + \sum \limits_{n=2}^{\infty }a_n(\;f\,)z^n $$ in a neighbourhood of the origin and map D onto a domain whose complement with respect to $\bar {{\bf C}}$ is convex. Let the set of these functions be denoted by Co . We fix | f m 1 ( X )| for f ] Co and determine the inner and outer radius of the ring domain which is the domain of variability of a 2 ( f ) for such f . Further, it is shown that f ] Co implies that $$ \phi (z) = z+2 {f'(z) \over f''(z)}$$ is holomorphic in D and maps D into itself. This implication in turn implies the inequalities | a n ( f )| S 1 for f ] Co and n = 2,3,4. In addition, we show that | a n ( f )| S 1/2 for f ] Co and all n S 2 . 相似文献
13.
Litan Yan 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):47-56
Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 . 相似文献
14.
A. V. Razgulin 《Computational Mathematics and Modeling》2000,11(1):46-55
We consider an initial-boundary-value problem for the nonlinear Schrödinger equation in the complexvalued functionE=E(x,z): (1) $\partial _z E + i\Delta E + i\alpha \left| E \right|^p E + \beta \left| E \right|^q E = 0, q > p \geqslant 0, \beta > 0,$ (2) $\left. E \right|_{z = 0} = E_0 \in H^2 (\Omega ) \cap H_0^1 (\Omega ), \left. E \right|_{\partial \Omega } = 0, \Omega \subset R^2 , \partial \Omega \in C^2 .$ We investigate the behavior of the solution of problem (1)–(2) as β→0 and its closeness to the solution of the degenerate equation (β=0). Given the consistency conditionq(β)=p+εln(1/β), 0≤?0, we establish boundedness of the norm $\left\| E \right\|_{C([0,z_0 ]):H_0^1 (\Omega ))} + \left\| {\partial _z E} \right\|_{C([0,z_0 ]);L^2 (\Omega ))} $ for every finitez 0>0 as β→0. For α≤0 and a fixedq, we prove uniform (in β) boundness of solutions of problem (1)–(2) on some interval [0,Z] and their convergence as β→0 to the solution of the degenerate problem (β=0) in the normC([0,Z];L 2 (Ω)). 相似文献
15.
设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点. 相似文献
16.
M. I. Gordin 《Journal of Mathematical Sciences》1999,93(3):311-320
Let (X, d) be a compact metric space, let T: X→X be a homeomorphism satisfying a certain suitable hyperbolicity assumption, and let μ be a Gibbs measure on X relative to T. Let λ be a complex number |λ|=1, and let f:X → ? be a Hölder continuous function. It is proved that $\sum\limits_{k \in \mathbb{Z}} {\lambda ^{ - k} } \left( {\int\limits_X {f(T^k x)\bar f(x)\mu (dx) - \left| {\int\limits_X {f(x)\mu (dx)} } \right|^2 } } \right) = 0$ if and only if ∑λ?k(f(Tky) ? f(Tkx)) = 0 for all x, y ε X such that $d(T^k x,T^k y)\xrightarrow[{|k| \to \infty }]{}0$ . Bibliography: 11 titles. 相似文献
17.
18.
《复变函数与椭圆型方程》2012,57(8):727-729
Let T ( f ) and N ( r,c ) denote the usual Nevanlinna characteristic and the counting function for the c -points of a meromorphic function f , respectively. Using a result of Miles and Shea ( Quart. J. Math. Oxford , 24 (2), (1973), 377-383) and two simple estimates for trigonometric functions, we show in connection with a 1929 problem of Nevanlinna for meromorphic functions f of finite order 1 < u < X $$ \limsup\limits_{r\rightarrow \infty } { N(r, 0)+N(r, \infty ) \over T(r, \,f)}\ge {2\sqrt 2 \over \pi} {|\sin \pi \lambda | \over D(\lambda )}\ge (0.9)\, {{|\sin \pi \lambda | \over {D(\lambda )}, }} $$ with D ( u ) = q +|sin ~ u | for $ q\le \lambda \le q + \fraca {1}{2} $ and D ( u ) = q + 1 for $ q + {\fraca {1} {2}} \le \lambda \lt q + 1 $ , where $ q = \lfloor \lambda \rfloor $ . 相似文献
19.
奇异半线性发展方程的局部Cauchy问题 总被引:9,自引:1,他引:8
本文在Banach空间E中讨论如下问题dudt+1tσAu=J(u),0<tT,limt→0+u(t)=0,其中u:(0,T]E,A是与t无关的线性算子.(-A)是E上C0半群{T(t)}t0的无穷小生成元,常数σ1,J是一个非线性映射EJ→E.它满足局部Lipschitz条件.我们证明了当其Lipschitz常数l(r)满足一定条件时.问题(S)有局部解,且在某函类中解唯一.设J(u)=|u|γ-1u+f(x)(γ>1),E=Lp,EJ=Lpγ时得到了与Weisler[2]在非奇异情形类似的结果. 相似文献
20.
Hu Ke 《数学年刊B辑(英文版)》1989,10(1):38-42
Let the function f(z)=z sum from n=2 to ∞ a_nz~n ∈ S. It is obtained that-2.793<|a_n 1|-|a_n|<3.26,which is an improvement of the result in [1] or [2]. 相似文献