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81.
Jenkinson Oliver; Gonzalez Luis Felipe; Urbanski Mariusz 《Proceedings London Mathematical Society》2003,86(3):755-778
For any non-empty subset I of the natural numbers, let I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator
for , where Re (rß) = I is the abscissa of convergence of the series . When acting on a certain Hilbert space HI, rß, weshow that the operator LI, rß is conjugate to an integraloperator KI, rß. If furthermore rß is real,then KI, rß is selfadjoint, so that LI, rß: HI, rß HI, rß has purely real spectrum.It is proved that LI, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß LI, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß LI, rß admits an analytic continuation beyond thehalf-plane Re rß > I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70. 相似文献
82.
J. Arvesú L. L. Littlejohn F. Marcellán 《Journal of Computational Analysis and Applications》2002,4(4):363-387
In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L2(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L2(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A1, first observed by Everitt, and the self-adjoint operator A1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A). 相似文献
83.
We construct the intertwining operator superalgebras and vertex tensor categories for the superconformal unitary minimal models and other related models.
84.
The theorems on weighted approximation and the order of approximation of continuous functions by modified Szasz—Mirakjan operators
on all positive semi-axis are established. 相似文献
85.
Resolution of composite fuzzy relation equations based on Archimedean triangular norms 总被引:1,自引:0,他引:1
Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max–min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm that is not Archimedean is the “minimum”. 相似文献
86.
S. Barry Cooper 《Mathematical Logic Quarterly》2001,47(1):3-33
A proof is given that 0 ′ (the argest Turing degree containing a computably enumerable set) is definable in the structure of the degrees of unsolvability. This answers a long‐standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator. 相似文献
87.
88.
V. T. Khudalov 《Mathematical Notes》2000,68(5-6):640-643
It is proved that the tensor product of two linear operators is a cone summing operator (respectively, order bounded operator) if and only if both operators are cone summing (respectively, order bounded). 相似文献
89.
Toeplitz algebras on discrete abelian quasily ordered groups 总被引:1,自引:0,他引:1
Xu Qingxiang 《Proceedings of the American Mathematical Society》2000,128(5):1405-1408
In this note, Toeplitz operators on discrete abelian quasily ordered groups are studied, and a theorem of R. Douglas is generalized.
90.
1. Introduction and NotationsThe generalized Feller operators which include many famous operators, such ajsBernstein, Szasz-Mirakjan, BaskakoV, Meyer--K5nig and Zeller operators, can be constructed by making use of the probabilistic method. In the paper [1][2], Xu JihuaPr(--lvjdetl a general scheme f(,r its construction, and Zhao Jillghui showed that theFeller type operators are of good approximations f'or unbounded functions.Our purpose is to present representation of moment generating … 相似文献