摘要:

AbstractUsing the result of almost u.d. mod 1 and G. Hoheisel [6] and Emdös's result, Akiyama [1]gave a different proof of the Erdös and Turán result [4], i.e., Δ2log pnchanges its sign infinitely many times, where pnis then‐th prime number and Δ2f(n) = Δ(Δf(n)), Δf(n) =f(n+ 1)‐f(n).In this paper, we show the neceasary condition for monotone almost uniform distribution mod 1. We give Fejér's type theorem for almost uniform distribution mod 1 and give a similar result of Niederreiter [8]. Also we obtain the converse of its result with some conditions. As an application, we give a simple proof [1]of Erdös and Turán's result using Erdös's result [cf. 3, 9, 10, 11, and 21. Also we obtain the condition ofP(n) that Δ2logP(n) changes its sign infin

ISSN:0025-584X    

DOI:10.1002/mana.3212050102

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractIn some weightedL2vector space we study a symmetric semibounded operator IL'0which is given by a 3 x 3 system of ordinary differential operators on an intervall [0, ro] with a singularity at r = 0 (see (0.1)). This system can be considered as a “smooth” perturbation of a more specific physical model describing the oscillations of plasma in an equilibrium configuration in a cylindrical domain (see (1.12)). This perturbation is smooth in the sense that in the system under study in comparison with the physical model only the smooth parts of the coefficients are changed conserving all types of singularities. It is the goal of this paper to construct a suitable selfadjoint extension IL of the symmetric operator IL'0(and its closure IL0) and to determine the essential spectrum of this extension. The essential spectrum consists of two bands (which may overlap) if we exclude the singularities by considering the system on an interval (r1,ro] with 0

ISSN:0025-584X    

DOI:10.1002/mana.3212050103

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractC. Herz introduced in [Hr]somenew spaces to study properties of functions. An Interesting account, with many applications, of some particular cases of the generalized Herz spaces is given in [BS]. In this paper we first identify the duals of the generalized Herz spaces. Then, we characterize their intermediate spaces when the complex method of interpolation for families of spaces Is used. Applications are given that show the bounded ness of many operators on the generalized Herz spaces.

ISSN:0025-584X    

DOI:10.1002/mana.3212050104

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractWe study linear ordinary differential equations near singular points of higher Poincaré rank r under the condition that the leading matrix has distinct eigenvalues. It is well known that there are fundamental systems of formal vector solutions and that in certain sectors, there are actual rolutions having those as asymptotic expansions.We study the corresponding remainders, in particular if the truncation pointNand the independent variablezare coupled such that Nzris approximately constant. We show that the remainders are exponentially small under this condition and how to choose the constant optimally. Furthermore, we obtain precise asymptotic expansions for these remainders.As corollaries, we obtain well known asymptotic expansions for the coefficients in the formal solutions and limit formulas for Stokes' multipliers.The method of proof only uses functions in the originalz‐ plane and its main tools are the Cauchy ‐Heine theorem and the saddle‐point

ISSN:0025-584X    

DOI:10.1002/mana.3212050105

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractWe show that every matrix valued generalized Nevanlinna function can be represented as au‐resolvent of a certain selfadjoint relation acting in a Pontryagin space. The negative index of this Pontryagin space may be larger than the number of negative squares of the given function. The minimal index of negative squares which is needed to obtain such a representation is determined. In the case of scalar functions, the results presented give rise to some new classes of generalized Nevanlinna function

ISSN:0025-584X    

DOI:10.1002/mana.3212050106

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractWe prove some general results on means of power type and their inequalities. Particularly, we study a new mean and compare this mean with the classical power means. Some results connected to compositions of power means are also presented. Our results are applied to some inequalities in the homogenization theory.

ISSN:0025-584X    

DOI:10.1002/mana.3212050107

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractIt is shown that if the dilatation tensorG fof a space quasi regular mappingfbelongs to the space VMO (vanishing mean oscillation), thenfis a local homeomorphism. The same is true If the BMO‐norm of Gfis small or if Gfis only close to the VMO space in the BMO‐n

ISSN:0025-584X    

DOI:10.1002/mana.3212050108

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

摘要:

AbstractA theorem of Calderón‐Vaillancourt type is obtained for a class of pseudodifferential sparators with operator‐valued symbols, and strongly continuous (in general non‐smooth) groups If isomorphisms involved in the symbol est

ISSN:0025-584X    

DOI:10.1002/mana.3212050109

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.3212050101

出版商:WILEY‐VCH Verlag    

年代:1999

数据来源: WILEY