共查询到20条相似文献,搜索用时 31 毫秒
1.
Radoslaw Czaja Messoud Efendiev 《Journal of Mathematical Analysis and Applications》2011,381(2):748-780
A family of compact and positively invariant sets with uniformly bounded fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the process is constructed. The existence of such a family, called a pullback exponential attractor, is proved for a nonautonomous semilinear abstract parabolic Cauchy problem. Specific examples will be presented in the forthcoming Part II of this work. 相似文献
2.
Abstract. Let be open,X a Banach space and . We show that every is holomorphic if and only if every set inX is bounded. Things are different if we assume f to be locally bounded. Then we show that it suffices that is holomorphic for all , where W is a separating subspace of to deduce that f is holomorphic. Boundary Tauberian convergence and membership theorems are proved. Namely, if boundary values (in a weak
sense) of a sequence of holomorphic functions converge/belong to a closed subspace on a subset of the boundary having positive
Lebesgue measure, then the same is true for the interior points of , uniformly on compact subsets. Some extra global majorants are requested. These results depend on a distance Jensen inequality.
Several examples are provided (bounded and compact operators; Toeplitz and Hankel operators; Fourier multipliers and small
multipliers).
Received January 29, 1998; in final form March 8, 1999 / Published online May 8, 2000 相似文献
3.
Alexander Brudnyi 《Inventiones Mathematicae》2013,193(1):187-227
We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H ∞ of bounded holomorphic functions on the unit disk $\mathbb{D}\subset \mathbb{C}$ with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H ∞, prove that the maximal ideal space of the algebra $H_{\mathrm{comp}}^{\infty}(A)$ of holomorphic functions on $\mathbb{D}$ with relatively compact images in a commutative unital complex Banach algebra A is homeomorphic to the direct product of maximal ideal spaces of H ∞ and A. 相似文献
4.
After proving a generalized version of Garkavi's theorem, we give as applications proofs of existence results on best approximation by polynomials, and fractional linear and holomorphic operators between Banach spaces. We also obtain theorems on best approximation by some types of rational functions defined in open subsets of Banach spaces. By considering a natural non-normable distance we prove that every mapping bounded on the bounded subsets of a Banach space has best approximation by polynomials of degree less than or equal to a fixed natural number n. 相似文献
5.
The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces
Erhan alkan 《Mathematische Nachrichten》2006,279(7):705-715
We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Fréchet–Schwartz space or (DFM )‐space E , then the space ??(U ) of holomorphic mappings on U , with the compact‐open topology, has the bounded approximation property if and only if E has the bounded approximation property. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set. 相似文献
7.
Multidimensional ultrametric pseudodifferential equations 总被引:1,自引:1,他引:0
We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined
as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and the
space D′0(X) of generalized functions on a multidimensional ultrametric space. We also consider some family of pseudodifferential operators
on multidimensional ultrametric spaces. The notions of Cauchy problem for ultrametric pseudodifferential equations and of
ultrametric characteristics are introduced. We prove an existence theorem and describe all solutions for the Cauchy problem
(an analog of the Kovalevskaya theorem). 相似文献
8.
《复变函数与椭圆型方程》2012,57(5):319-321
Let X be a topological space whose topology may be defined by a complete metric d. Taking all such metrics d we define a universal complex structure on X. For this complex structure the sheaf of germs of holomorphic functions on X coincides with the sheaf of germs of continuous functions on X, and hence the theories of topological and holomorphic vector bundles on X are the same. 相似文献
9.
Ngaiming Mok 《中国科学A辑(英文版)》2008,51(4):660-684
In 1993,Tsal proved that a proper holomorphic mapping f:Ω→Ω' from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ' is necessarily totally geodesic provided that r':=rank(Ω')≤rank(Ω):= r,proving a conjecture of the author's motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents(VMRTs). In another completely different direction Hwang-Mok established with very few exceptions the Cartan- Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num- ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio- nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com- plex Grassmann manifolds of rank≤2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin's which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures. 相似文献
10.
We consider the following problem: let V? be a finite dimensional vector space, and U be a compact group of ?‐linear automorphisms of V?. The polynomial envelope of a compact set Q ? V? is defined as where ??(V?) denotes the space of holomorphic polynomial functions on V?. The problem is to determine the polynomial envelope of a compact set which is U‐invariant. We solve the problem when U is the isotropy subgroup at the origin of the automorphism group of a bounded symmetric domain of tube type. The case of a domain of type II has been solved by C. Sacré [1992], and, for a domain of type IV, it has been solved by L. Bou Attour [1993]. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Gerald Beer 《Topology and its Applications》2008,155(6):503-514
Call a sequence in a metric space cofinally Cauchy if for each positive ε there exists a cofinal (rather than residual) set of indices whose corresponding terms are ε-close. We give a number of new characterizations of metric spaces for which each cofinally Cauchy sequence has a cluster point. For example, a space has such a metric if and only each continuous function defined on it is uniformly locally bounded. A number of results exploit a measure of local compactness functional that we introduce. We conclude with a short proof of Romaguera's Theorem: a metrizable space admits such a metric if and only if its set of points having a compact neighborhood has compact complement. 相似文献
12.
Yves Bolle 《Expositiones Mathematicae》2001,19(1)
The equivalence between the Cauchy left-integrability and the Riemann-integrability, for a bounded function defined on a compact interval of with values in a Banach space, is a particular case of Theorem 2.1. A first generalization to the case of functions defined on a compact rectangle of 2 is given by Theorem 2.5. 相似文献
13.
We study a class of examples of negatively curved compact Kähler surfaces that are not diffeomorphic to any locally symmetric space. From the analysis of certain totally geodesic curves on these surfaces we deduce that, for infinitely many examples, the natural representation of the fundamental group into PU(2,1) is non-faithful. We also give a new construction of bounded holomorphic functions on the universal cover of our surfaces, based on lifting maps to compact Riemann surfaces. 相似文献
14.
高明杵 《数学物理学报(B辑英文版)》1998,(1)
0IntroductionIn[1],deLaubenfelsdefilledexpollelltiitllyboullded11olonlorphicC-existeuccfalllilies,holomorpllicC-senhgroupsand11olonlorpllicilltegratedselnigroups.Healsodiscussedtheirrelationships,alldgavesomeHille-YOsidatypecollditiollsforalloperatortogenerateallyofthesefamiliesofoperatorsin[1].ZllengalldLetdefinedexpollelltiallyboulldedllololllorphiconceilltegratedC-semigroups,andpreselltedageueratiolltlleorelllill[2J.Moregelleral71-tilllesintegratedmildC-existencefamilieswereintroducedby… 相似文献
15.
We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem. 相似文献
16.
The bornology (b) of bounded subsets with respect to continuous convergence is used on spaces of holomorphic functions. It is shown that HomcoHb(U) ? U for a circled convex open subset U of a complete nuclear space. Exponential laws for spaces of holomorphic functions with bornological structures are proved and the connection with Colombeau's Silva holomorphic functions is established. 相似文献
17.
We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary
condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is
also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators
on small spaces. We also prove the converse of Shapiro’s theorem if the symbol function is already contained in the space
under consideration. In the course of the proofs we characterize the bounded composition operators on the Zygmund class. Also,
as a by-product of our arguments, we show that small holomorphic Sobolev spaces are algebras. 相似文献
18.
Sebastian Król 《Semigroup Forum》2009,79(2):369-376
We show that every contractive C
0-semigroup on a separable, infinite-dimensional Hilbert space X can be approximated by unitary C
0-groups in the weak operator topology uniformly on compact subsets of ℝ+. As a consequence we get a new characterization of a bounded H
∞-calculus for the negatives of generators of bounded holomorphic semigroups. Applications of our results to the study of a
topological structure of the set of (almost) weakly stable contractive C
0-semigroups on X are also discussed.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr. N201384834. 相似文献
19.
Denote by the family of all real valued functions on a metric space which satisfy a Lipschitz condition on the compact (bounded) subsets of X. We prove that every homomorphism on is the evaluation at some point of X if and only if X is realcompact (every closed bounded subset of X is compact).
(Received 4 November 1998; in revised form 31 May 1999) 相似文献
20.
V. N. Razzhevaikin 《Differential Equations》2013,49(3):320-325
We consider the Cauchy problem for the reaction-nonlinear diffusion equation in a space of arbitrary dimension. On the basis of the original data of the equation, we compute the potential function, whose maximum corresponds to a dominant equilibrium distribution. For the solutions of the problem with initial distributions in a rather broad class, we prove the convergence to the dominant distribution on bounded subsets. 相似文献