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1.
In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.  相似文献   

2.
Schilling  René L. 《Positivity》1998,2(3):239-256
Let denote a Feller semigroup on , and itsextension to the bounded measurable functions. We show that . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.  相似文献   

3.
A basis is constructed inc 0 such that there exists no bounded linear projection ofc 0 onto the subspace spanned by a certain subsequence of . This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice.  相似文献   

4.
The sequence of orthogonal polynomials is said to be classical if is also orthogonal. The aim of this paper is to find the sequences which have the property that is also orthogonal. We prove that sequences, with this property have to be, classical and belong either to the set of Laguerre or Jacobi polynomials, where in the Laguerre case c has to be zero and in the Jacobi case c = ±1.  相似文献   

5.
6.
We consider the series and whose coefficients satisfy the condition for , where the sequence can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If as , then the series is uniformly convergent. If for all , then the sequence of partial sums of this series is uniformly bounded. If the series is convergent for and as , then this series is uniformly convergent. If the sequence of partial sums of the series for is bounded and for all , then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence is lacunary. In the general case, they are not necessary.  相似文献   

7.
For a Dirichlet series with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder , < 0, as n .  相似文献   

8.
The following classes of functions analytic in the unit disk are considered:
and
where is the Nevanlinna characteristic and is a properly changing positive function on (0,1]. Necessary and sufficient conditions on are established under which the classes and are invariant under the operators of differentiation and integration. Bibliography: 7 titles.  相似文献   

9.
Summary Let be a real irreduciblen×n interval matrix. Then a necessary and sufficient condition is given for the sequence of the powers of an interval matrix to converge to a matrix which is not the null matrix. In addition a criterion for is proved to decide whether the limit matrix satisfies the condition of symmetry .  相似文献   

10.
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let be a system of distinct points on and let be the family of all systems of nonoverlapping simply connected domains on such that . Let
where is the reduced module of the domain with respect to the point . At present, the problem concerning the value was solved completely for . In this work, we continue the previous author's investigations and consider the case . In addition, we consider the problem concerning the maximum of the sum
in the family introduced above, where , are arbitrary points of the circle , and is a positive number. We prove that if , then the maximum is attained only for systems of equidistant points of the circle . For , this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if , where is an even number, then equidistant points of the circle do not realize the indicated maximum. Bibliography: 11 titles.  相似文献   

11.
Summary We study the problem of the existence of bounded solutions for the equation on pseudo-Siegel domains when the data satisfies the condition .
Sunto Si studia il problema dell'esistenza di soluzioni limitate per l'equazione sui domini pseudo-Siegel quando il dato soddisfa alla condizione .


Work done within the Project 40% M.U.R.S.T. «Geometria Reale e Complessa».  相似文献   

12.
We study sets there exist n projectors P1,...,Pn such that . We prove that if n 6, then .  相似文献   

13.
From the Erds–Turán theorem, it is known that if f is a continuous function on and L n (f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in and continuous on and making use of algebraic interpolating polynomials in the roots of unity.In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on .  相似文献   

14.
A renormalization group transformation R 1 has a single stable point in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number (the golden mean). Let a homeomorphism T be the C 1-conjugate of . We let denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any , the sequence has a finite limiting distribution function , which is continuous in , and singular on the interval [0,1]. We also study the sequence for k>1.  相似文献   

15.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let be a rational prime, an exact category. In this article, we define and study for all , the profinite higher K-theory of , that is as well as , where is the -dimensional mod- Moore space. We study connections between and prove several -completeness results involving these and associated groups including the cases where is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of .  相似文献   

16.
Let be sequences of real numbers which are symmetric in k. Let be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of we consider
Let
Several examples are given in which the condition
is either a sufficient, a necessary, or a necessary and sufficient condition for {Q(x), x[0, 2] n } to have a continuous version.  相似文献   

17.
Ouhabaz  El Maati 《Positivity》1999,3(1):83-93
Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.  相似文献   

18.
Dehornoy constructed a right invariant order on the braid group B n uniquely defined by the condition 1{\text{ if }}\beta _0 ,\beta _1$$ " align="middle" border="0"> are words in . A braid is called strongly positive if 1$$ " align="middle" border="0"> for any . In the present paper it is proved that the braid is strongly positive if the word does not contain . We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity.  相似文献   

19.
Pekarskii  A. A. 《Mathematical Notes》2002,72(1-2):230-236
In the open disk of the complex plane, we consider the following spaces of functions: the Bloch space ; the Hardy--Sobolev space ; and the Hardy--Besov space . It is shown that if all the poles of the rational function R of degree n, , lie in the domain , then , where and depends only on . The second of these inequalities for the case of the half-plane was obtained by Semmes in 1984. The proof given by Semmes was based on the use of Hankel operators, while our proof uses the special integral representation of rational functions.  相似文献   

20.
Quasiconcave functions and belong to the same scale if there exist quasiconcave functions and and numbers such that and . We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences.  相似文献   

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