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1.
Suppose that p(X, Y) = A − BX − X(∗)B(∗) − CYC(∗) and q(X, Y) = A − BX + X(∗)B(∗) − CYC(∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y(∗), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y = −Y(∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed. 相似文献
2.
Two perturbation estimates for maximal positive definite solutions of equations X + A*X−1A = Q and X − A*X−1A = Q are considered. These estimates are proved in [Hasanov et al., Improved perturbation Estimates for the Matrix Equations X ± A*X−1A = Q, Linear Algebra Appl. 379 (2004) 113-135]. We derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations. The theoretical results are illustrated by numerical examples. 相似文献
3.
Akinari Hoshi 《Journal of Number Theory》2011,131(11):2135-2150
Let m?−1 be an integer. We give a correspondence between integer solutions to the parametric family of cubic Thue equations
X3−mX2Y−(m+3)XY2−Y3=λ 相似文献
4.
Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Fréchet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X* and Y*) are isomorphic? We prove that if X* or Y* has the approximation property and Hwu(U) and Hwu(V) are topologically algebra isomorphic, then X* and Y* are isomorphic (the converse being true when U and V are the whole space). We get analogous results for Hb(U) and Hb(V), giving conditions under which an algebra isomorphism between Hb(X) and Hb(Y) is equivalent to an isomorphism between X* and Y*. We also obtain characterizations of different algebra homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on Hb(X) with pathological behaviors. 相似文献
5.
This paper concerns polynomials in g noncommutative variables x=(x1,…,xg), inverses of such polynomials, and more generally noncommutative “rational expressions” with real coefficients which are formally symmetric and “analytic near 0.” The focus is on rational expressions r=r(x) which are “matrix convex” near 0; i.e., those rational expressions r for which there is an ?>0 such that if X=(X1,…,Xg) is a g-tuple of n×n symmetric matrices satisfying
6.
A Banach spaceX is non-quasi-reflexive (i.e. dimX **/X=∞) if and only if it contains a basic sequence spanning a non-quasi-reflexive subspace. In fact, this basic sequence can be chosen to be non-k-boundedly complete for allk. A basic sequence which is non-k-shrinking for allk exists inX if and only ifX * contains a norming subspace of infinite codimension. This need not occur even ifX is non-quasi-reflexive. Every norming subspace ofX * has finite codimension if and only if for every normingM inX *, everyM-closedY inX,M∩Y T is norming overX/Y. This solves a problem due to Schäffer [19]. 相似文献
7.
Volker Ziegler 《Journal of Number Theory》2006,120(2):303-325
We consider the relative Thue inequalities
|X4−t2X2Y2+s2Y4|?2|t|−2|s|−2, 相似文献
8.
A.B.J. Kuijlaars K.T.-R. McLaughlin W. Van Assche M. Vanlessen 《Advances in Mathematics》2004,188(2):337-398
We consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1−x)α(1+x)βh(x), with α,β>−1 and h real analytic and strictly positive on [−1,1]. We obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval [−1,1], for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials. We also deduce asymptotic behavior for the Hankel determinants and for the monic orthogonal polynomials on the interval [−1,1]. For the asymptotic analysis we use the steepest descent technique for Riemann-Hilbert problems developed by Deift and Zhou, and applied to orthogonal polynomials on the real line by Deift, Kriecherbauer, McLaughlin, Venakides, and Zhou. In the steepest descent method we will use the Szeg? function associated with the weight and for the local analysis around the endpoints ±1 we use Bessel functions of appropriate order, whereas Deift et al. use Airy functions. 相似文献
9.
Xian Zhang 《Journal of Applied Mathematics and Computing》2004,14(1-2):51-67
A matrix pair (X 0,Y 0) is called a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation $$GXG* + HYH* = C$$ with unknownX andY ifX 0 andY 0 are Hermitian nonnegative-definite (respectively, positive-definite) and satisfyGX 0G*+HY0H*=C. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach. 相似文献
10.
Yuan Gong Sun 《Journal of Mathematical Analysis and Applications》2003,279(2):651-658
Some new oscillation criteria are established for the matrix linear Hamiltonian system X′=A(t)X+B(t)Y, Y′=C(t)X−A∗(t)Y under the hypothesis: A(t), B(t)=B∗(t)>0, and C(t)=C∗(t) are n×n real continuous matrix functions on the interval [t0,∞), (−∞<t0). These results are sharper than some previous results even for self-adjoint second order matrix differential systems. 相似文献
11.
N.G. Ushakov 《Statistics & probability letters》2011,81(5):614-617
In this note we present one characterization of symmetry of probability distributions in Euclidean spaces which is formulated as follows. Let X and Y be independent and identically distributed random elements in a separable Euclidean space E. If Eeh|X|<∞, h>0, then the distribution of X is symmetric if and only if E|(X−Y,t)|p=E|(X+Y,t)|p for some 0<p<2 and for any t∈E. The criterion is not correct when at least one of the conditions 0<p<2 or Eeh|X|<∞ breaks. 相似文献
12.
Manuel González 《Archiv der Mathematik》2011,97(4):345-352
The perturbation classes problem for semi-Fredholm operators asks when the equalities SS(X,Y)=PF+(X,Y){\mathcal{SS}(X,Y)=P\Phi_+(X,Y)} and SC(X,Y)=PF-(X,Y){\mathcal{SC}(X,Y)=P\Phi_-(X,Y)} are satisfied, where SS{\mathcal{SS}} and SC{\mathcal{SC}} denote the strictly singular and the strictly cosingular operators, and PΦ+ and PΦ− denote the perturbation classes for upper semi-Fredholm and lower semi-Fredholm operators. We show that, when Y is a reflexive Banach space, SS(Y*,X*)=PF+(Y*,X*){\mathcal{SS}(Y^*,X^*)=P\Phi_+(Y^*,X^*)} if and only if SC(X,Y)=PF-(X,Y),{\mathcal{SC}(X,Y)=P\Phi_-(X,Y),} and SC(Y*,X*)=PF-(Y*,X*){\mathcal{SC}(Y^*,X^*)=P\Phi_-(Y^*,X^*)} if and only if SS(X,Y)=PF+(X,Y){\mathcal{SS}(X,Y)=P\Phi_+(X,Y)}. Moreover we give examples showing that both direct implications fail in general. 相似文献
13.
周云华 《数学物理学报(B辑英文版)》2011,31(1):102-108
Let T : X → X be a uniformly continuous homeomorphism on a non-compact metric space (X, d). Denote by X* = X ∪ {x*} the one point compactification of X and T * : X* → X* the homeomorphism on X* satisfying T *|X = T and T *x* = x*. We show that their topological entropies satisfy hd(T, X) ≥ h(T *, X*) if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space. 相似文献
14.
Elói Medina Galego 《Journal of Mathematical Analysis and Applications》2008,338(1):653-661
We first introduce the notion of (p,q,r)-complemented subspaces in Banach spaces, where p,q,r∈N. Then, given a couple of triples {(p,q,r),(s,t,u)} in N and putting Λ=(q+r−p)(t+u−s)−ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p,q,r)-complemented in Y and Y is (s,t,u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds:
- (a)
- Λ≠0, Λ divides p−q and s−t, p=1 or q=1 or s=1 or t=1.
- (b)
- p=q=s=t=1 and gcd(r,u)=1.
15.
N. Hadjisavvas D. Kravvaritis G. Pantelidis I. Polyrakis 《Rendiconti del Circolo Matematico di Palermo》1989,38(1):130-139
LetX be a topological vector space,Y an ordered topological vector space andL(X,Y) the space of all linear and continuous mappings fromX intoY. The hereditary order-convex cover [K] h of a subsetK ofL(X,Y) is defined by [K] h ={A∈L(X,Y):Ax∈[Kx] for allx∈X}, where[Kx] is the order-convex ofKx. In this paper we study the hereditary order-convex cover of a subset ofL(X,Y). We show how this cover can be constructed in specific cases and investigate its structural and topological properties. Our results extend to the spaceL(X,Y) some of the known properties of the convex hull of subsets ofX *. 相似文献
16.
H. Yokota 《Journal of Number Theory》2010,130(9):2003-2010
Let D=F2+2G be a monic quartic polynomial in Z[x], where . Then for F/G∈Q[x], a necessary and sufficient condition for the solution of the polynomial Pell's equation X2−DY2=1 in Z[x] has been shown. Also, the polynomial Pell's equation X2−DY2=1 has nontrivial solutions X,Y∈Q[x] if and only if the values of period of the continued fraction of are 2, 4, 6, 8, 10, 14, 18, and 22 has been shown. In this paper, for the period of the continued fraction of is 4, we show that the polynomial Pell's equation has no nontrivial solutions X,Y∈Z[x]. 相似文献
17.
Assume that X and Y are Hermitian solutions to quaternion matrix equation AXA ?+BYB ?=C, which are partitioned into 2×2 block forms. We in this paper give the maximal and minimal ranks of submatrices in the Hermitian solutions X=X ?, Y=Y ?, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. The findings of this paper widely extend the known results in the literature. 相似文献
18.
Given a vector measure ν with values in a Banach space X, we consider the space L1(ν) of real functions which are integrable with respect to ν. We prove that every order continuous Banach function space Y continuously contained in L1(ν) is generated via a certain positive map related to ν and defined on X* x M, where X* is the dual space of X and M the space of measurable functions. This procedure provides a way of defining Orlicz spaces with respect to the vector measure ν. 相似文献
19.
András Vasy 《Advances in Mathematics》2010,223(1):49-97
In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X○,g) which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y±, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to +∞, and to the other manifold as the parameter goes to −∞, we also define the scattering operator, and show that it is a Fourier integral operator associated to the bicharacteristic flow from Y+ to Y−. 相似文献
20.
Rainer Siegmund-Schultze 《Advances in Mathematics》2007,208(2):672-679
We prove for an arbitrary random walk in R1 with independent increments that the probability of crossing a level at a given time n is O(n−1/2). Moment or symmetry assumptions are not necessary. In removing symmetry the (sharp) inequality P(|X+Y|?1)<2P(|X−Y|?1) for independent identically distributed X,Y is used. In part II we shall discuss the connection of this result to ‘polygonal recurrence’ of higher-dimensional walks and some conjectures on directionally reinforced random walks in the sense of Mauldin, Monticino and von Weizsäcker [R.D. Mauldin, M. Monticino, H. von Weizsäcker, Directionally reinforced random walks, Adv. Math. 117 (1996) 239-252. [5]]. 相似文献