共查询到20条相似文献,搜索用时 46 毫秒
1.
Let K be a complete ultrametric algebraically closed field and let A be the K-Banach algebra of bounded analytic functions in the disk . Let Mult(A,‖⋅‖) be the set of continuous multiplicative semi-norms of A, let Multm(A,‖⋅‖) be the subset of the ?∈Mult(A,‖⋅‖) whose kernel is a maximal ideal and let Multa(A,‖⋅‖) be the subset of the ?∈Multm(A,‖⋅‖) whose kernel is of the form (if ?∈Multm(A,‖⋅‖)?Multa(A,‖⋅‖), the kernel of ? is then of infinite codimension). The main problem we examine is whether Multa(A,‖⋅‖) is dense inside Multm(A,‖⋅‖) with respect to the topology of simple convergence. This a first step to the conjecture of density of Multa(A,‖⋅‖) in the whole set Mult(A,‖⋅‖): this is the corresponding problem to the well-known complex corona problem. We notice that if ?∈Multm(A,‖⋅‖) is defined by an ultrafilter on D, ? lies in the closure of Multa(A,‖⋅‖). Particularly, we shaw that this is case when a maximal ideal is the kernel of a unique ?∈Multm(A,‖⋅‖). Thus, if every maximal ideal is the kernel of a unique ?∈Multm(A,‖⋅‖), Multa(A,‖⋅‖) is dense in Multm(A,‖⋅‖). And particularly, this is the case when K is strongly valued. In the general context, we find a subset of Multm(A,‖⋅‖)?Multa(A,‖⋅‖) which is included in the closure of Multa(A,‖⋅‖). More generally, we show that if ψ∈Mult(A,‖⋅‖) does not define the Gauss norm on polynomials (‖⋅‖), then it is characterized by a circular filter, like on rational functions and analytic elements. As a consequence, if ψ does not lie in the closure of Multa(A,‖⋅‖), then its restriction to polynomials is the Gauss norm. 相似文献
2.
Let Mn(R) be the linear space of all n×n matrices over the real field R. For any A∈Mn(R), let ρ(A) and ‖A‖∞ denote the spectral radius and the infinity norm of A, respectively. By introducing a class of transformations φa on Mn(R), we show that, for any A∈Mn(R), ρ(A)<‖A‖∞ if . If A∈Mn(R) is nonnegative, we prove that ρ(A)<‖A‖∞ if and only if , and ρ(A)=‖A‖∞ if and only if the transformation φ‖A‖∞ preserves the spectral radius and the infinity norm of A. As an application, we investigate a class of linear discrete dynamic systems in the form of X(k+1)=AX(k). The asymptotical stability of the zero solution of the system is established by a simple algebraic method. 相似文献
3.
For 0<p<+∞ let hp be the harmonic Hardy space and let bp be the harmonic Bergman space of harmonic functions on the open unit disk U. Given 1?p<+∞, denote by ‖⋅bp‖ and ‖⋅hp‖ the norms in the spaces bp and hp, respectively. In this paper, we establish the harmonic hp-analogue of the known isoperimetric type inequality ‖fb2p‖?‖fhp‖, where f is an arbitrary holomorphic function in the classical Hardy space Hp. We prove that for arbitrary p>1, every function f∈hp satisfies the inequality
‖fb2p‖?ap‖fhp‖, 相似文献
4.
Harris Kwong 《Discrete Mathematics》2008,308(23):5522-5532
Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f∗:E→A defined by f∗(xy)=f(x)+f(y). For i∈A, let vf(i)=card{v∈V:f(v)=i} and ef(i)=card{e∈E:f∗(e)=i}. A labeling f is said to be A-friendly if |vf(i)−vf(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |ef(i)−ef(j)|≤1 for all (i,j)∈A×A. When A=Z2, the friendly index set of the graph G is defined as {|ef(1)−ef(0)|:the vertex labelingf is Z2-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4). 相似文献
5.
Consider two circle homeomorphisms fi∈C2+α(S?{bi}), α>0, i=1,2 with a single break point bi i.e. a discontinuity in the derivative Dfi, and identical irrational rotation number ρ. Suppose the jump ratios and do not coincide. Then the map ψ conjugating f1 and f2 is a singular function i.e. it is continuous on S1 and Dψ(x)=0 a.e. with respect to Lebesgue measure. 相似文献
6.
László Lovász 《Journal of Combinatorial Theory, Series A》2006,113(4):726-735
We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1,f2 defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)fi(A)+μ(B)fi(B)+μ(A∪B)fi(A∪B)+μ(A∩B)fi(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this. 相似文献
7.
Smaïl Djebali 《Journal of Mathematical Analysis and Applications》2009,353(1):215-672
This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Δu(x)+f(x,u(x))+g(‖x‖)x⋅∇u(x)=0, x∈Rn, ‖x‖>R. We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f(x,0)≡0. The asymptotic behavior of solutions is also described. 相似文献
8.
Let N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=limn→∞|A∩[1,n]|/n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let SN denote the set of all permutations of the positive integers N. The group L? consists of all permutations f∈SN such that A∈AD if and only if f(A)∈AD, and the group L* consists of all permutations f∈L? such that d(f(A))=d(A) for all A∈AD. Let be a one-to-one function such that d(f(N))=1 and, if A∈AD, then f(A)∈AD. It is proved that f must also preserve density, that is, d(f(A))=d(A) for all A∈AD. Thus, the groups L? and L* coincide. 相似文献
9.
M. Fabian 《Journal of Mathematical Analysis and Applications》2008,339(1):735-739
Let (X,‖⋅‖) be a reflexive Banach space with Kadec-Klee norm. Let f:X→(−∞,+∞] be a function which is either Lipschitzian or is proper, bounded below, and lower semi-continuous. Then f is supported from below by residually many parabolas opening downward, that is, the infimal convolution of ‖⋅‖2 and f is attained at residually many points of X. 相似文献
10.
Ciprian G. Gal 《Journal of Mathematical Analysis and Applications》2007,333(2):971-983
In this paper we consider the nonlinear differential equation with deviated argument u′(t)=Au(t)+f(t,u(t),u[φ(u(t),t)]), t∈R+, in a Banach space (X,‖⋅‖), where A is the infinitesimal generator of an analytic semigroup. Under suitable conditions on the functions f and φ, we prove a global existence and uniqueness result for the above equation. 相似文献
11.
A.B. Aleksandrov 《Journal of Functional Analysis》2010,258(11):3675-5251
This is a continuation of our paper [2]. We prove that for functions f in the Hölder class Λα(R) and 1<p<∞, the operator f(A)−f(B) belongs to Sp/α, whenever A and B are self-adjoint operators with A−B∈Sp. We also obtain sharp estimates for the Schatten-von Neumann norms ‖f(A)−f(B)Sp/α‖ in terms of ‖A−BSp‖ and establish similar results for other operator ideals. We also estimate Schatten-von Neumann norms of higher order differences . We prove that analogous results hold for functions on the unit circle and unitary operators and for analytic functions in the unit disk and contractions. Then we find necessary conditions on f for f(A)−f(B) to belong to Sq under the assumption that A−B∈Sp. We also obtain Schatten-von Neumann estimates for quasicommutators f(A)R−Rf(B), and introduce a spectral shift function and find a trace formula for operators of the form f(A−K)−2f(A)+f(A+K). 相似文献
12.
Stacey Muir 《Journal of Mathematical Analysis and Applications》2008,348(2):862-871
For two complex-valued harmonic functions f and F defined in the open unit disk Δ with f(0)=F(0)=0, we say f is weakly subordinate to F if f(Δ)⊂F(Δ). Furthermore, if we let E be a possibly infinite interval, a function with f(⋅,t) harmonic in Δ and f(0,t)=0 for each t∈E is said to be a weak subordination chain if f(Δ,t1)⊂f(Δ,t2) whenever t1,t2∈E and t1<t2. In this paper, we construct a weak subordination chain of convex univalent harmonic functions using a harmonic de la Vallée Poussin mean and a modified form of Pommerenke's criterion for a subordination chain of analytic functions. 相似文献
13.
Let F be a field and let m and n be integers with m,n?3. Let Mn denote the algebra of n×n matrices over F. In this note, we characterize mappings ψ:Mn→Mm that satisfy one of the following conditions:
- 1.
- |F|=2 or |F|>n+1, and ψ(adj(A+αB))=adj(ψ(A)+αψ(B)) for all A,B∈Mn and α∈F with ψ(In)≠0.
- 2.
- ψ is surjective and ψ(adj(A-B))=adj(ψ(A)-ψ(B)) for every A,B∈Mn.
14.
Let S={x1,…,xn} be a set of n distinct positive integers. For x,y∈S and y<x, we say the y is a greatest-type divisor of x in S if y∣x and it can be deduced that z=y from y∣z,z∣x,z<x and z∈S. For x∈S, let GS(x) denote the set of all greatest-type divisors of x in S. For any arithmetic function f, let (f(xi,xj)) denote the n×n matrix having f evaluated at the greatest common divisor (xi,xj) of xi and xj as its i,j-entry and let (f[xi,xj]) denote the n×n matrix having f evaluated at the least common multiple [xi,xj] of xi and xj as its i,j-entry. In this paper, we assume that S is a gcd-closed set and . We show that if f is a multiplicative function such that (f∗μ)(d)∈Z whenever and f(a)|f(b) whenever a|b and a,b∈S and (f(xi,xj)) is nonsingular, then the matrix (f(xi,xj)) divides the matrix (f[xi,xj]) in the ring Mn(Z) of n×n matrices over the integers. As a consequence, we show that (f(xi,xj)) divides (f[xi,xj]) in the ring Mn(Z) if (f∗μ)(d)∈Z whenever and f is a completely multiplicative function such that (f(xi,xj)) is nonsingular. This confirms a conjecture of Hong raised in 2004. 相似文献
15.
Xie Ping Ding 《Journal of Mathematical Analysis and Applications》2005,305(1):29-42
Let I be a finite or infinite index set, X be a topological space and (Yi,{φNi})i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature. 相似文献
16.
On Montel's theorem and Yang's problem 总被引:1,自引:0,他引:1
Yan Xu 《Journal of Mathematical Analysis and Applications》2005,305(2):743-751
Let F be a family of meromorphic functions defined in a domain D, and let ψ be a function meromorphic in D. For every function f∈F, if (1)f has only multiple zeros; (2) the poles of f have multiplicity at least 3; (3) at the common poles of f and ψ, the multiplicity of f does not equal the multiplicity of ψ; (4)f(z)≠ψ(z), then F is normal in D. This gives a partial answer to a problem of L. Yang, and generalizes Montel's theorem. Some examples are given to show the sharpness of our result. 相似文献
17.
For digraphs D and H, a mapping f:V(D)→V(H) is a homomorphism ofDtoH if uv∈A(D) implies f(u)f(v)∈A(H). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by a real-world problem in defence logistics and was introduced recently by the authors and M. Tso.Suppose we are given a pair of digraphs D,H and a cost ci(u) for each u∈V(D) and i∈V(H). The cost of a homomorphism f of D to H is ∑u∈V(D)cf(u)(u). Let H be a fixed digraph. The minimum cost homomorphism problem for H, MinHOMP(H), is stated as follows: For input digraph D and costs ci(u) for each u∈V(D) and i∈V(H), verify whether there is a homomorphism of D to H and, if it does exist, find such a homomorphism of minimum cost. In our previous paper we obtained a dichotomy classification of the time complexity of when H is a semicomplete digraph. In this paper we extend the classification to semicomplete k-partite digraphs, k≥3, and obtain such a classification for bipartite tournaments. 相似文献
18.
Thomas H. Pate 《Linear algebra and its applications》2010,432(1):116-133
Let V be a complex inner product space of positive dimension m with inner product 〈·,·〉, and let Tn(V) denote the set of all n-linear complex-valued functions defined on V×V×?×V (n-copies). By Sn(V) we mean the set of all symmetric members of Tn(V). We extend the inner product, 〈·,·〉, on V to Tn(V) in the usual way, and we define multiple tensor products A1⊗A2⊗?⊗An and symmetric products A1·A2?An, where q1,q2,…,qn are positive integers and Ai∈Tqi(V) for each i, as expected. If A∈Sn(V), then Ak denotes the symmetric product A·A?A where there are k copies of A. We are concerned with producing the best lower bounds for ‖Ak‖2, particularly when n=2. In this case we are able to show that ‖Ak‖2 is a symmetric polynomial in the eigenvalues of a positive semi-definite Hermitian matrix, MA, that is closely related to A. From this we are able to obtain many lower bounds for ‖Ak‖2. In particular, we are able to show that if ω denotes 1/r where r is the rank of MA, and , then
19.
20.
Raphaël M. Jungers Vladimir Protasov Vincent D. Blondel 《Linear algebra and its applications》2008,428(10):2296-2311
For a given finite set Σ of matrices with nonnegative integer entries we study the growth with t of
max{‖A1?At‖:Ai∈Σ}. 相似文献