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31.
A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators. 相似文献
32.
Márcia Federson 《Czechoslovak Mathematical Journal》2002,52(2):429-437
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil,
, where R is a compact interval of
, and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral,
, as well as to unbounded intervals R. 相似文献
33.
Harry Kesten R. A. Maller 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》1999,35(6):685
We show that the passage time, T*(r), of a random walk Sn above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that
as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that
as n→∞ for a deterministic sequence Bn>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞. 相似文献
34.
Andreas E. Schroth 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):211-227
Every flat Laguerre plane that satisfies a certain variation of the Miquel Condition is ovoidal. Equivalently, in flat Laguerre
planes a certain special version of the Bundle Theorem already implies the Bundle Theorem. 相似文献
35.
Olaf Bröcker 《Journal of Geometry》2002,75(1-2):46-60
For M?bius planes Schaeffer [9] has proved that all seven
point degenerations of Miquel's Theorem characterize miquelian M?bius
planes. For Laguerre planes we have several degenerations of Miquel's
Theorem with eight and seven points. We prove that all except one of
these degenerations characterize miquelian Laguerre planes. The
remaining degeneration characterizes elation Laguerre planes.
Received 14 September 2001; revised 1 September 2002. 相似文献
36.
The theorem of Hohenberg and Kohn is extended to subdomains of a bounded quantum system. It is shown that the ground state
particle density of an arbitrary subdomain uniquely determines the ground state properties of this subdomain, of any other
subdomain, and of the total domain of the system. 相似文献
37.
Jinlu Li 《Journal of Mathematical Analysis and Applications》2004,295(1):115-126
In this paper, we study the existence of the solution of the variational inequality 〈Tx−ξ,y−x〉?0 by applying the generalized projection operator , where B is a Banach space with dual space B∗ and by using the well-known FanKKM Theorem. 相似文献
38.
Peter A. Loeb Horst Osswald Yeneng Sun Zhixiang Zhang 《Transactions of the American Mathematical Society》2004,356(8):3209-3225
For a square integrable vector-valued process on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for are presented. The process is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for involving the biorthogonal representation for the conditional expectation of with respect to the usual product -algebra is presented.
39.
We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n
r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open. 相似文献
40.
Christopher Meaney 《Proceedings of the American Mathematical Society》2003,131(10):3123-3128
We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .