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1.
Operator Matrix Forms of Positive Operators   总被引:2,自引:0,他引:2  
If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2)of operators on Hibert spaces is given,we proved that the operator ~↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R(A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet.  相似文献   

2.
Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.  相似文献   

3.
1. IntroductionLet Rmxn denote the set of m x n real matrices, s: dellote the at of n x n positive delhatereal symmetric matrices. For A = (a.) and B = (hi,) E Rm", the Hadamard product of Aand B is defined as an m x n matriX denoted by A o B: (A o B). = a.bt,.We write A 2 B if at; 2 hi, for all i,j. A real n x n matriX A is called a nonsingularM-~ac if A = sl ~ B satisfied: 8 > 0, B 2 0 and 8 > P(B), the spectral rebus of B, let Madenote the s6t of all n x n nonsingular M-mstrices…  相似文献   

4.
In this paper,the zeros of solutions of periodic second order linear differential equation y + Ay = 0,where A(z) = B(e z ),B(ζ) = g(ζ) + p j=1 b ?j ζ ?j ,g(ζ) is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.  相似文献   

5.
A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1 , X B 1 = C 3 , A 2 X = C 2 , X B 2 = C 4 , A 3 X B 3 = C 5 , A 4 X B 4 = C 6 which was investigated recently by Wang, Chang and Ning (Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195: 721-732 (2008)). Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.  相似文献   

6.
蒋立宁  郭懋正 《数学进展》2003,32(2):239-240
A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A).  相似文献   

7.
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.  相似文献   

8.
Main ResultLet P be the distribution of a one-dimensional Brownian motion (Bt,) with drift8 starting at B0 = 0. A Brownian motion (Bt, ) on a circle of unit circumference can beobtained as Bt = Bt mod 1, where the circle is identified with [0, 1]. The local time processof B is , where Z is the set of integers, and is the usual bicontinuous local time process of B, normalized as occupation density relativeto Lebesgue measure. Let C ([0, 1)) be the space of nonnegative continuous paths wit…  相似文献   

9.
In this paper we prove the following theorem.It is a generalization of Tenchel's theorem on theintegral curvature of curve.Theorem.If 1 is the length of a curve C=AB and φ is the angle between the tangent vectors ofC at A,B,then the integral curvature of C  相似文献   

10.
Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=PABPA*,where PA and PA*denote projections onto the closures of R(A)and R(A*),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions.  相似文献   

11.
In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of Cm+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that
is a U(m)-connection of ℱ(m,n) and its curvature form
satisfies the Yang-Mills equation. Moreover,
is an (Sum)-connection and its curvature form
satisfies the Yang-Mills equation. Project partially supported by the National Natural Science Foundation of China (Grant No. 19631010) and Fundamental Research Bureau of CAS.  相似文献   

12.
For functions satisfying the boundary conditions
, the following inequality with sharp constants in additive form is proved:
wheren≥2, 0≤1≤n−2,−1≤m≤1, m+1≤n−3, and1≤p,q,r≤∞. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 712–724, November, 1997. Translated by N. K. Kulman  相似文献   

13.
Asymptotic expansions in the two limitsx → + ∞ andx → 0+ are obtained for the Mehler-Fock transform
  相似文献   

14.
We prove the existence of a transformation operator that takes the solution of the equationy″=λ2n y to the solution of the equation
with a condition at infinity. Some properties of the kernel of this operator are studied. Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 206–215, August, 1997. Translated by M. A. Shishkova  相似文献   

15.
Suppose that a lower triangular matrix μ:[μ m (n) ] defines a conservative summation method for series, i.e.,
and the sequence (ρ m ,m ∈ ℤ0), is bounded away from zero. Then the trigonometric series is the Fourier series of a functionfL p ( ), wherep ε ]1; ∞[, if and only if the sequence ofp-norms of its μ-means is bounded:
In the case of the Fejér method, we have the test due to W. and G. Young (1913). In the case of the Fourier method, we obtain the converse of the Riesz theorem (1927). Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 677–686, November, 1997. Translated by N. K. Kulman  相似文献   

16.
Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x f(t,x)=0 are given by means of variational methods, where the function -1/2a(t)|s|^2∫^t0f(t,s)ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t 1 t a(t)dt= ∞,VI∈R^1.A resonance case as well as a noncompact case is discussed too.  相似文献   

17.
We study the solvability of the integral equation
, wherefL 1 loc(ℝ) is the unknown function andg,T 1, andT 2 are given functions satisfying the conditions
. Most attention is paid to the nontrivial solvability of the homogeneous equation
. Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997. Translated by M. A. Shishkova  相似文献   

18.
For an entire Dirichlet series , sufficient conditions on the exponents are established such that the following relations hold outside a set of finite measure asx→+∞:
, where ψ(x) is a function increasing to +∞ and such thatx≤ψ(x)≤e x (x≥0). Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 282–292, August, 1999  相似文献   

19.
GLOBAL ATTRACTIVITY IN A DISCRETE DELAY LOGISTIC MODEL   总被引:1,自引:0,他引:1  
1.IntroductionIntherecentworks[l--31,theauthorsconsideredthediscretedelaylogisticmodelIn[3],itwasshownthateverypositivesolutionof(l)oscillatesaboutitspositiveequilibriumx~(a--1)/0ifandonlyifIn[if(seealso[2]),itwasprovedthatiftheneverypositivesolutionof(1)tendstox~(or--1)/pasn-- co.Thepurposeofthispaperistoobtainanothersufficieatconditionforthepositiveequilibriumxof(1)tobeaglobalattractorbyusingamethodverydmerelltfromthatusedin[1,21.Themainresultofthispaperisthefollowingtheorem.*Thisworkispart…  相似文献   

20.
A trace formula expressing the mean values of the form (k=2,3,...)
via certain arithmetic means on the group Г0(N1) is proved. Here the sum is taken over a normalized orthogonal basis in the space of holomorphic cusp forms of weight 2k with respect to Г0(N1). By H f (x) (s) we denote the Hecke series of the form f, twisted with the primitive character χ (mod N2), and λf(d), (d, N1N2)=1, are the eigenvalues of the Hecke operators
. The trace formula is used for obtaining the estimate
for the newform f for all ε>0, l=0,1,2,.... This improves the known result (Duke-Friedlander-Iwaniec, 1993) with upper bound (1+|t|)2N 2 1/2−1/22+ε on the right-hand side. As a corollary, we obtain the estimate
for the Fourier coefficients of holomorphic cusp forms of weight k+1/2, which improves Iwaniec' result (1987) with exponent 1/4–1/28+ε. Bibliography: 25 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 14–36.  相似文献   

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