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1.
One of the main results of the present article is as follows Theorem. Let v: Ω → ? be a C1-smooth function on a domain Ω ? ?2. Suppose that Int?v(Ω) = ?. Then, for every point z ∈ Ω, there is a straight line L ? z such that ?v ≡ const on the connected component of the set L ? Ω containing z.Also, we prove that, under the conditions of the theorem, the range of the gradient ?v(Ω) is locally a curve and this curve has tangents in the weak sense and the direction of these tangents is a function of bounded variation.  相似文献   

2.
We classify graph C *-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C *-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence of such algebras, without using the boundary operator algebra. A direct relation is given between the K 1-group of the algebra and the cycle space of the graph. We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K 0( Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University College.  相似文献   

3.
This paper is a survey on the Hyers–Ulam–Rassias stability of the following Cauchy–Jensen functional equation in C *-algebras:
The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem (Rassias in Proc. Am. Math. Soc. 72:297–300, [1978]). This work was supported by the research fund of Hanyang University (HY-2007-S).  相似文献   

4.
Stochastic partial differential equations of divergence form are considered in C1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.Mathematics Subject Classification (2000): 60H15, 35R60  相似文献   

5.
In this paper, we get W 1,p (R n )-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and Tananka’s results. Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural Science Foundation of China.  相似文献   

6.
Let
be a C*-discrete quantum group and let
be the discrete quantum group associated with
. Suppose that there exists a continuous action of
on a unital C*-algebra
so that
becomes a
-algebra. If there is a faithful irreducible vacuum representation π of
on a Hilbert space H =
with a vacuum vector Ω, which gives rise to a
-invariant state, then there is a unique C*-representation (θ, H) of
supplemented by the action. The fixed point subspace of
under the action of
is exactly the commutant of θ(
).
  相似文献   

7.
For any 0 < ? < 1 one can find a measurable set E ? [0, 1] with the measure |E| > 1 ? ? such that for each function f(x) ε L 1 (0, 1) a function g(x) ε L 1 (0, 1) exists such that it coincides with f (x) on E, its Fourier—Walsh series converges to it in the metric of L 1 (0, 1), and all nonzero terms of the sequence of Fourier coefficients of the new function obtained by the Walsh system have the modulo decreasing order; consequently, the greedy algorithm for this function converges to it in the L 1 (0, 1)-norm.  相似文献   

8.
Themba Dube 《Order》2008,25(4):369-375
We characterise C*-quotients and C-quotients of completely regular frames in terms of ?ech-Stone compactifications and Lindelöfications, respectively. The latter is a frame-theoretic result with no spatial counterpart. We also characterise C*-quotients and dense C-quotients of completely regular frames in terms of normal covers.  相似文献   

9.
It is known that not every Cantor set of S 1 is C 1-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C 1-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C 1+∈-minimal, for any ∈ > 0. Partially supported by CNPq-Brasil and PEDECIBA-Uruguay.  相似文献   

10.
We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if has a unit e, then for every x, yV and every ɛ > 0 there are contractions u, υ ∊ such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.   相似文献   

11.
Let R be a real AW *-algebra, and suppose that its complexification M = R + iR is also a (complex) AW *-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov  相似文献   

12.
The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras.  相似文献   

13.
We find some necessary and sufficient conditions for a plane curve to be the gradient range of a C 1-smooth function of two variables. As one of the consequences we give the necessary and sufficient conditions on a continuous function ? under which the differential equation \(\frac{{\partial v}}{{\partial t}} = \varphi \left( {\frac{{\partial v}}{{\partial x}}} \right)\) has nontrivial C 1-smooth solutions.  相似文献   

14.
Let A be a separable simple C*-algebra. For each ;) on A such that π(a) has a non-trivial invariant subspace in Hπ.  相似文献   

15.
L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1R 1 and ∈ L loc p (R n ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L p (K) with any accuracy for any compact set K in R n , if and only if g(x) is not an even polynomial. Partly supported by the National Natural Science Foundation of China (10471017)  相似文献   

16.
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra into a unital C*-algebra ℬ are homomorphisms when f(2 n uy) = f(2 n u)f(y), g(2 n uy) = g(2 n u)g(y) and h(2 n uy) = h(2 n u)h(y) hold for all unitaries u ∈ , all y ∈ , and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2 n uy) = f(2 n u)f(y), g(2 n uy) = g(2 n u)g(y) and h(2 n uy) = h(2 n u)h(y) hold for all u ∈ {v ∈ : v = v* and v is invertible}, all y ∈ and all n ∈ ℤ. Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras. This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008. The second author was supported by the Brain Korea 21 Project in 2005.  相似文献   

17.
We construct an example of a C 1-smooth real function of two variables whose gradient range is an arc with no tangent at any point.  相似文献   

18.
In this paper we obtain local L p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)  相似文献   

19.
In this paper we use the real differential geometric definition of a metric (a unimodular oriented metric) tt*-bundle of Cortés and the author (Topological-anti-topological fusion equations, pluriharmonic maps and special Kähler manifolds) to define a map Φ from the space of metric (unimodular oriented metric) tt*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to {GL}(r)/O(p,q) (respectively {SL}(r)/SO(p,q)), where (p,q) is the signature of the metric. In the sequel the image of the map Φ is characterized. It follows, that in signature (r,0) the image of Φ is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin (Comm. Math. Phys. 152 (1992; S539–S564).  相似文献   

20.
In this paper we obtain a Chernoff-type approximation theorem for C-semigroups, from which we derive the Trotter product formula and the Post-Widder inversion formula for C-semigroups. The first author was supported by the NSF of China (Grant No. 10501032) and the NSFC-RFBR Programm (Grant No. 108011120015), and the second author by the NSF of China (Grant No. 10671079).  相似文献   

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