共查询到20条相似文献,搜索用时 46 毫秒
1.
Let D be a bounded n-dimensional domain, ∂D be its boundary, be its closure, T be a positive real number, B be an n-dimensional ball {x∈D:|x−b|<R} centered at b∈D with a radius R, be its closure, ∂B be its boundary, ν denote the unit inward normal at x∈∂B, and χB(x) be the characteristic function. This article studies the following multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source occupying :
2.
For n∈N and D⊆N, the distance graph has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of a Hamiltonian cycle are all equivalent. Our main result suitably extends this equivalence to distance graphs. We prove that for a finite set D of order at least 2, there is a constant cD such that the greatest common divisor of the integers in D is 1 if and only if for every n, has a component of order at least n−cD if and only if for every n≥cD+3, has a cycle of order at least n−cD. Furthermore, we discuss some consequences and variants of this result. 相似文献
3.
Julie Yeramian 《Journal of Pure and Applied Algebra》2009,213(6):1013-1025
4.
Rosihan M. Ali V. Ravichandran 《Journal of Mathematical Analysis and Applications》2006,324(1):663-668
Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that
5.
Serban T. Belinschi 《Advances in Mathematics》2008,217(1):1-41
Let Dc(k) be the space of (non-commutative) distributions of k-tuples of selfadjoint elements in a C∗-probability space. On Dc(k) one has an operation ? of free additive convolution, and one can consider the subspace of distributions which are infinitely divisible with respect to this operation. The linearizing transform for ? is the R-transform (one has Rμ?ν=Rμ+Rν, ∀μ,ν∈Dc(k)). We prove that the set of R-transforms can also be described as {ημ|μ∈Dc(k)}, where for μ∈Dc(k) we denote ημ=Mμ/(1+Mμ), with Mμ the moment series of μ. (The series ημ is the counterpart of Rμ in the theory of Boolean convolution.) As a consequence, one can define a bijection via the formula
(I) 相似文献
6.
7.
Jian-Lin Li 《Journal of Functional Analysis》2008,255(11):3125-3148
The self-affine measure μM,D corresponding to an expanding matrix M∈Mn(R) and a finite subset D⊂Rn is supported on the attractor (or invariant set) of the iterated function system {?d(x)=M−1(x+d)}d∈D. The spectral and non-spectral problems on μM,D, including the spectrum-tiling problem implied in them, have received much attention in recent years. One of the non-spectral problem on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D) and to find them. In the present paper we show that if a,b,c∈Z, |a|>1, |c|>1 and ac∈Z?(3Z),
8.
Patrick Ahern 《Journal of Functional Analysis》2004,215(1):206-216
We study the range of the Berezin transform B. More precisely, we characterize all triples (f,g,u) where f and g are non-constant holomorphic functions on the unit disc D in the complex plane and u is integrable on D such that . It turns out that there are very ‘few’ such triples. This problem arose in the study of Bergman space Toeplitz operators and its solution has application to the theory of such operators. 相似文献
9.
Stephan Ruscheweyh Luis Salinas 《Journal of Mathematical Analysis and Applications》2004,291(2):596-604
An analytic function f(z) in the unit disc D is called stable if sn(f,·)/f?1/f holds for all for . Here sn stands for the nth partial sum of the Taylor expansion about the origin of f, and ? denotes the subordination of analytic functions in . We prove that (1−z)λ, λ∈[−1,1], are stable. The stability of turns out to be equivalent to a famous result of Vietoris on non-negative trigonometric sums. We discuss some generalizations of these results, and related conjectures, always with an eye on applications to positivity results for trigonometric and other polynomials. 相似文献
10.
11.
Maria Monks 《Discrete Mathematics》2009,309(16):5196-1883
All continuous endomorphisms f∞ of the shift dynamical system S on the 2-adic integers Z2 are induced by some , where n is a positive integer, Bn is the set of n-blocks over {0, 1}, and f∞(x)=y0y1y2… where for all i∈N, yi=f(xixi+1…xi+n−1). Define D:Z2→Z2 to be the endomorphism of S induced by the map {(00,0),(01,1),(10,1),(11,0)} and V:Z2→Z2 by V(x)=−1−x. We prove that D, V°D, S, and V°S are conjugate to S and are the only continuous endomorphisms of S whose parity vector function is solenoidal. We investigate the properties of D as a dynamical system, and use D to construct a conjugacy from the 3x+1 function T:Z2→Z2 to a parity-neutral dynamical system. We also construct a conjugacy R from D to T. We apply these results to establish that, in order to prove the 3x+1 conjecture, it suffices to show that for any m∈Z+, there exists some n∈N such that R−1(m) has binary representation of the form or . 相似文献
12.
For 0<p,α<∞, let ‖f‖p,α be the Lp-norm with respect the weighted measure . We define the weighted Bergman space Aαp(D) consisting of holomorphic functions f with ‖f‖p,α<∞. For any σ>0, let A−σ(D) be the space consisting of holomorphic functions f in D with . If D has C2 boundary, then we have the embedding Aαp(D)⊂A−(n+α)/p(D). We show that the condition of C2-smoothness of the boundary of D is necessary by giving a counter-example of a convex domain with C1,λ-smooth boundary for 0<λ<1 which does not satisfy the embedding. 相似文献
13.
14.
Let D=G/K be an irreducible bounded symmetric domain of dimension d and let be the analytic continuation of the weighted Bergman spaces of holomorphic functions on D. We consider the d-tuple M=(M1,…,Md) of multiplication operators by coordinate functions and consider its spectral properties. We find those parameters ν for which the tuple M is subnormal and we answer some open questions of Bagchi and Misra. In particular, we prove that when D=Bd is the unit ball in , then Bd is a k-spectral set of M if and only if is the Hardy space or a weighted Bergman space. 相似文献
15.
Chris Lennard 《Journal of Mathematical Analysis and Applications》2009,350(1):384-392
We study certain Hardy-type sequence spaces Hp and , 1?p?∞, which are analogues of ?∞ and c0, respectively. We show that the Mazur product is not onto for every p∈(1,∞) with q=p−1(p−1). We present corollaries for spaces defined via weighted ?p seminorms and for c0. The latter corollary provides a new solution of Mazur's Problem 8 in the Scottish Book. 相似文献
16.
17.
Qian Lu 《Journal of Mathematical Analysis and Applications》2008,340(1):394-400
We consider the normality criterion for a families F meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each z∈Δ, such that there not only exists a positive number ε0 such that |an(a(z)−1)−1|?ε0 for arbitrary sequence of integers an(n∈N) and for any z∈Δ, but also exists a positive number B>0 such that for every f(z)∈F, B|f′(z)|?|f(z)| whenever f(z)f″(z)−a(z)(f′2(z))=0 in Δ. Then is normal in Δ. 相似文献
18.
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
19.
Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
20.
Let B be the unit ball of with respect to an arbitrary norm. We study certain properties of Loewner chains and their transition mappings on the unit ball B. We show that any Loewner chain f(z,t) and the transition mapping v(z,s,t) associated to f(z,t) satisfy locally Lipschitz conditions in t locally uniformly with respect to z∈B. Moreover, we prove that a mapping f∈H(B) has parametric representation if and only if there exists a Loewner chain f(z,t) such that the family {e−tf(z,t)}t?0 is a normal family on B and f(z)=f(z,0) for z∈B. Also we show that univalent solutions f(z,t) of the generalized Loewner differential equation in higher dimensions are unique when {e−tf(z,t)}t?0 is a normal family on B. Finally we show that the set S0(B) of mappings which have parametric representation on B is compact. 相似文献