共查询到20条相似文献,搜索用时 31 毫秒
1.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
2.
Simon Wassermann 《Journal of Functional Analysis》1976,23(3):239-254
If A and B are C1-algebras there is, in general, a multiplicity of C1-norms on their algebraic tensor product A ⊙ B, including maximal and minimal norms ν and α, respectively. A is said to be nuclear if α and ν coincide, for arbitrary B. The earliest example, due to Takesaki [11], of a nonnuclear C1-algebra was , the C1-algebra generated by the left regular representation of the free group on two generators F2. It is shown here that W1-algebras, with the exception of certain finite type I's, are nonnuclear.If is the group C1-algebra of F2, there is a canonical homomorphism λl of onto . The principal result of this paper is that there is a norm ζ on , distinct from α, relative to which the homomorphism is bounded ( being endowed with the norm α). Thus quotients do not, in general, respect the norm α; a consequence of this is that the set of ideals of the α-tensor product of C1-algebras A and B may properly contain the set of product ideals {}.Let A and B be C1-algebras. If A or B is a W1-algebra there are on A ⊙ B certain C1-norms, defined recently by Effros and Lance [3], the definitions of which take account of normality. In the final section of the paper it is shown by example that these norms, with α and ν, can be mutually distinct. 相似文献
3.
A.M Fink 《Journal of Mathematical Analysis and Applications》1977,61(2):404-408
We show how inequalities of the type when F(0) = 0 can be used to find lower bounds of the first eigenvalue of the integral equation F(z) = λ ∝0ak(s, z)F(s) ds. 相似文献
4.
J.E Nymann 《Journal of Number Theory》1975,7(4):406-412
Given a set S of positive integers let denote the number of k-tuples 〈m1, …, mk〉 for which and (m1, …, mk) = 1. Also let denote the probability that k integers, chosen at random from , are relatively prime. It is shown that if P = {p1, …, pr} is a finite set of primes and S = {m : (m, p1 … pr) = 1}, then if k ≥ 3 and where d(S) denotes the natural density of S. From this result it follows immediately that as n → ∞. This result generalizes an earlier result of the author's where and S is then the whole set of positive integers. It is also shown that if S = {p1x1 … prxr : xi = 0, 1, 2,…}, then as n → ∞. 相似文献
5.
Let be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in nn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). 相似文献
6.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
7.
Alain A. Lewis 《Mathematical Social Sciences》1985,9(2):189-194
Let be an ω1-saturated enlargement in the sense of Keisler (1977) and let be a hyperfinite finite set in 1. Following the suggestion of Wesley (1971) we define a class of hyperfinite games of the form: , and show that measure-theoretic analogues of the kernel and bargaining set exist in this nonstandard setting such that their standard parts Loeb-measurable measurable on the Loeb space generated by the internal 1finitely additive measure . 相似文献
8.
Let Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of elements in Fn, and s(Fn) be the number of singular matrices in Fn. We prove that if n ? 2, and if n = 2 and o(F) ? 3, then . 相似文献
9.
Ming-Po Chen Cheh-Chih Yeh Cheng-Shu Yu 《Journal of Mathematical Analysis and Applications》1977,59(2):211-215
For nonlinear retarded differential equations and the sufficient conditions are given on fi, pi, Fi, and h under which every bounded nonoscillatory solution of () or () tends to zero as t → ∞. 相似文献
10.
The existence, uniqueness, and construction of unitary n × n matrix valued functions in Wiener-like algebras on the circle with prescribed matrix Fourier coefficients for j ? 0 are studied. In particular, if , then such an ? exists with if and only if ∥Γ0∥ ? 1, where Γv, denotes the infinite block Hankel matrix (γj + k + v), j, k = 0, 1,…, acting in the sequence space ln2. One of the main results is that the nonnegative factorization indices of every such ? are uniquely determined by the given data in terms of the dimensions of the kernels of , whereas the negative factorization indices are arbitrary. It is also shown that there is a unique such ? if and only if the data forces all the factorization indices to be nonnegative and simple conditions for that and a formula for ? in terms of certain Schmidt pairs of Γ0 are given. The results depend upon a fine analysis of the structure of the kernels of and of the one step extension problem of Adamjan, Arov, and Krein (Funct. Anal. Appl.2 (1968), 1–18). Isometric interpolants for the nonsquare case are also considered. 相似文献
11.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
12.
Anne Marie Torpe 《Journal of Functional Analysis》1985,61(1):15-71
The K-theory of the C1-algebra associated to C∞-foliations (V, F) of a manifold V in the simplest non-trivial case, i.e., dim V = 2, is studied. Since the case of the Kronecker foliation was settled by Pimsner and Voiculescu (J. Operator Theory4 (1980), 93–118), the remaining problem deals with foliations by Reeb components. The K-theory of for the Reeb foliation of S3 is also computed. In these cases the C1-algebra is obtained from simpler C1-algebras by means of pullback diagrams and short exact sequences. The K-groups are computed using the associated Mayer-Vietoris and six-term exact sequences. The results characterize the C1-algebra of the Reeb foliation of 2 uniquely as an extension of C(S1) by C(S1). For the foliations of 2 it is found that the K-groups count the number of Reeb components separated by stable compact leaves. A C∞-foliation of 2 such that K1(C1(2, F)) has infinite rank is also constructed. Finally it is proved, by explicit calculation using (M. Penington, “K-Theory and C1-Algebras of Lie Groups and Foliations,” D. Phil. thesis, Oxford, 1983), that the natural map is an isomorphism for foliations by Reeb components of 2 and S3. In particular this proves the Baum-Connes conjecture (P. Baum and A. Connes, Geometric K-theory for Lie groups, preprint, 1982; A. Connes, Proc. Symp. Pure Math.38 (1982), 521–628) when V = 2. 相似文献
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15.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
16.
Yuh-Jia Lee 《Journal of Functional Analysis》1982,47(2):153-164
Let (H, B) be an abstract Wiener pair and pt the Wiener measure with variance t. Let a be the class of exponential type analytic functions defined on the complexification [B] of B. For each pair of nonzero complex numbers α, β and f ? a, we define We show that the inverse α,β?1 exists and there exist two nonzero complex numbers α′,β′ such that . Clearly, the Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of α,β. Finally, we apply the transform to investigate the existence of solutions for the differential equations associated with the operator c, where c is a nonzero complex number and c is defined by where Δ is the Laplacian and (·, ·) is the pairing. We show that the solutions can be represented as integrals with respect to the Wiener measure. 相似文献
17.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
18.
Let Fn(x) be the empirical distribution function based on n independent random variables X1,…,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm, and an invariance principle for . 相似文献
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20.
J Bustoz 《Journal of Mathematical Analysis and Applications》1981,79(1):71-79
It is known that the classical orthogonal polynomials satisfy inequalities of the form Un2(x) ? Un + 1(x) Un ? 1(x) > 0 when x lies in the spectral interval. These are called Turan inequalities. In this paper we will prove a generalized Turan inequality for ultraspherical and Laguerre polynomials. Specifically if Pnλ(x) and Lnα(x) are the ultraspherical and Laguerre polynomials and . We also prove the inequality is a positive constant depending on α and β. 相似文献