共查询到20条相似文献,搜索用时 406 毫秒
1.
Allan M Krall 《Journal of Differential Equations》1977,24(2):253-267
This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in np[0,1] × np[0,1], 1 ? p < ∞. The adjoint relation in nq[0,1] × nq[0,1], , is derived. Green's formula is also found. Self-adjoint relations are found in n2[0,1] × n2[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of np[0,1] × n2[0,1] is established. 相似文献
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Let and denote respectively the space of n×n complex matrices and the real space of n×n hermitian matrices. Let p,q,n be positive integers such that p?q?n. For , the (p,q)-numerical range of A is the set , where Cp(X) is the pth compound matrix of X, and Jq is the matrix Iq?On-q. Let denote n or . The problem of determining all linear operators T: → such that is treated in this paper. 相似文献
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The main concern of this paper is linear matrix equations with block-companion matrix coefficients. It is shown that general matrix equations AX ? XB = C and X ? AXB = C can be transformed to equations whose coefficients are block companion matrices: and , respectively, where ?L and CM stand for the first and second block-companion matrices of some monic r × r matrix polynomials L(λ) = λsI + Σs?1j=0λjLj and M(λ) = λtI + Σt7minus;1j=0λjMj. The solution of the equat with block companion coefficients is reduced to solving vector equations Sx = ?, where the matrix S is r2l × r2l[l = max(s, t)] and enjoys some symmetry properties. 相似文献
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Allan J. Sieradski 《Topology》1978,17(1):85-93
THIS PAPER investigates the structure of the semigroup Σ generated by a set S of non-cancellation examples in the homotopy category. The featured spaces are the 3-dimensional Lens spaces Lp.q. Their products Lp.q × S3 with the 3-sphere S3 are shown to have the same simple-homotopy type, while their own products are shown to determine a unique-division semigroup. 相似文献
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Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
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《Stochastic Processes and their Applications》1987,24(2):279-286
For every positive integer n, let Sn be the n-th partial sum of a sequence of independent and identically distributed random variables, each assuming the values +1 and −1 with respective probabilities p (0<p<1)) and q (= 1 −p) and having mean μ = p − q. For a fixed positive real number λ, let N+[N1] be the total number of values of n for which Sn > (μ + λ)n [Sn⩾(μ + λ)n] and let L+[L1] be the supremum of the values of n for which Sn > (μ + λ)n [Sn⩾(μ + λ)n], where sup Oslash; = 0. Explicit expressions for the exact distributions of N+, N1, L+ and L1 are given when μ + λ = ±k/(k + 2) for any nonnegative integer k. 相似文献
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J. V. Brawley 《Linear algebra and its applications》1975,10(3):199-217
Let F=GF(q) denote the finite field of order q, and let . Then f(x) defines, via substitution, a function from Fn×n, the n×n matrices over F, to itself. Any function which can be represented by a polynomialf(x)?F[x] is called a scalar polynomial function on Fn×n. After first determining the number of scalar polynomial functions on Fn×n, the authors find necessary and sufficient conditions on a polynomial in order that it defines a permutation of (i) n, the diagonalizable matrices in Fn×n, (ii)n, the matrices in Fn×n all of whose roots are in F, and (iii) the matric ring Fn×n itself. The results for (i) and (ii) are valid for an arbitrary field F. 相似文献
9.
Hermann König 《Journal of Functional Analysis》1977,24(1):32-51
For an open set Ω ? N, 1 ? p ? ∞ and λ ∈ +, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm (cf. A. Pietsch, “r-nukleare Sobol. Einbett. Oper., Ellipt. Dgln. II,” Akademie-Verlag, Berlin, 1971, pp. 203–215). Choose a Banach ideal of operators , 1 ? p, q ? ∞ and a quasibounded domain Ω ? N. Theorem 1 of the note gives sufficient conditions on λ such that the Sobolev-imbedding map exists and belongs to the given Banach ideal : Assume the quasibounded domain fulfills condition Ckl for some l > 0 and 1 ? k ? N. Roughly this means that the distance of any to the boundary ?Ω tends to zero as for , and that the boundary consists of sufficiently smooth ?(N ? k)-dimensional manifolds. Take, furthermore, 1 ? p, q ? ∞, p > k. Then, if μ, ν are real positive numbers with λ = μ + v ∈ , μ > λ S(; p,q:N) and v > N/l · λD(;p,q), one has that belongs to the Banach ideal . Here λD(;p,q;N)∈+ and λS(;p,q;N)∈+ are the D-limit order and S-limit order of the ideal , introduced by Pietsch in the above mentioned paper. These limit orders may be computed by estimating the ideal norms of the identity mappings lpn → lqn for n → ∞. Theorem 1 in this way generalizes results of R. A. Adams and C. Clark for the ideals of compact resp. Hilbert-Schmidt operators (p = q = 2) as well as results on imbeddings over bounded domains.Similar results over general unbounded domains are indicated for weighted Sobolev spaces.As an application, in Theorem 2 an estimate is given for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω fulfills condition C1l.For an open set Ω in N, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm, see below. Taking a fixed Banach ideal of operators and 1 ? p, q ? ∞, we consider quasibounded domains Ω in N and give sufficient conditions on λ such that the Sobolev imbedding operator exists and belongs to the Banach ideal. This generalizes results of C. Clark and R. A. Adams for compact, respectively, Hilbert-Schmidt operators (p = q = 2) to general Banach ideals of operators, as well as results on imbeddings over bounded domains. Similar results over general unbounded domains may be proved for weighted Sobolev spaces. As an application, we give an estimate for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω is a quasibounded open set in N. 相似文献
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Let Fm×nq denote the vector space of all m×n matrices over the finite field Fq of order q, and let denote an ordered basis for Fm×nq. If the rank of Ai is ri,i=1,2,…,mn, then is said to have rank (r1,r2,…,rmn), and the number of ordered bases of Fmxnq with rank (r1,r2,…,rmn is denoted by Nq(r1, r2,…,rmn). This paper determines formulas for the numbers Nq(r1,r2,…,rmn) for the case m=n=2, q arbitrary, and while some of the techniques of the paper extend to arbitrary m and n, the general formulas for the numbers Nq(r1,r2,…,rmn) seem quite complicated and remain unknown. An idea on a possible computer attack which may be feasible for low values of m and n is also discussed. 相似文献
11.
Daniel J. Madden 《Journal of Number Theory》1978,10(3):303-323
If k is a perfect field of characteristic p ≠ 0 and k(x) is the rational function field over k, it is possible to construct cyclic extensions Kn over k(x) such that [K : k(x)] = pn using the concept of Witt vectors. This is accomplished in the following way; if [β1, β2,…, βn] is a Witt vector over k(x) = K0, then the Witt equation generates a tower of extensions through where . In this paper, it is shown that there exists an alternate method of generating this tower which lends itself better for further constructions in Kn. This alternate generation has the form Ki = Ki?1(yi); yip ? yi = Bi, where, as a divisor in Ki?1, Bi has the form . In this form q is prime to Πpjλj and each λj is positive and prime to p. As an application of this, the alternate generation is used to construct a lower-triangular form of the Hasse-Witt matrix of such a field Kn over an algebraically closed field of constants. 相似文献
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The Schur product of two n×n complex matrices A=(aij), B=(bij) is defined by A°B=(aijbij. By a result of Schur [2], the algebra of n×n matrices with Schur product and the usual addition is a commutative Banach algebra under the operator norm (the norm of the operator defined on n by the matrix). For a fixed matrix A, the norm of the operator B?A°B on this Banach algebra is called the Schur multiplier norm of A, and is denoted by ∥A∥m. It is proved here that for all unitary U (where ∥·∥ denotes the operator norm) iff A is a scalar multiple of a unitary matrix; and that ∥A∥m=∥A∥ iff there exist two permutations P, Q, a p×p (1?p?n) unitary U, an (n?p)×(n?p)1 contraction C, and a nonnegative number λ such that and this is so iff , where ā is the matrix obtained by taking entrywise conjugates of A. 相似文献
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Melvyn B. Nathanson 《Journal of Number Theory》2003,103(2):214-233
For the quantum integer [n]q=1+q+q2+?+qn−1 there is a natural polynomial multiplication such that [m]q⊗q[n]q=[mn]q. This multiplication leads to the functional equation fm(q)fn(qm)=fmn(q), defined on a given sequence of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation. 相似文献
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Let L ≠ Kinp be a p-chromatic graph and e be an edge of L such that L ? e is (p?1)-chromatic If Gn is a graph of n vertices without containing L but containing Kp, then the minimum valence of Gn is 相似文献
18.
Let V be an n-dimensional vector space over Fq. Let Φ be a Hermitian form with respect to an automorphism σ with σ2 = 1. If σ = 1 assume that q is odd. Let be the arrangement of hyperplanes of V which are non-isotropic with respect to Φ, and let L be the intersection lattice of . We prove that the characteristic polynomial of L has n ? v roots 1, q,…, qn ? v? 1 where v is the Witt index of Φ. 相似文献
19.
David S Jerison 《Journal of Functional Analysis》1981,43(1):97-142
For (x,y,t)∈n × n × , denote and . When α = n ? 2q, a represents the action of the Kohn Laplacian □b on q-forms on the Heisenberg group. For ?n < α < n, we construct a parametrix for the Dirichlet problem in smooth domains D near non-characteristic points of ?D. A point w of ?D is non-characteristic if one of X1,…, Xn, Y1,…, Yn is transverse to ?D at w. This yields sharp local estimates in the Dirichlet problem in the appropriate non-isotropic Lipschitz classes. The main new tool is a “convolution calculus” of pseudo-differential operators that can be applied to the relevant layer potentials, for which the usual asymptotic composition formula is false. Characteristic points are treated in Part II. 相似文献
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《Journal of Computational and Applied Mathematics》2002,139(2):253-274
Let {Snλ} denote the monic orthogonal polynomial sequence with respect to the Sobolev inner productwhere {dψ0,dψ1} is a so-called coherent pair and λ>0. Then Snλ has n different, real zeros. The position of these zeros with respect to the zeros of other orthogonal polynomials (in particular Laguerre and Jacobi polynomials) is investigated. Coherent pairs are found where the zeros of Sn−1λ separate the zeros of Snλ. 相似文献