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931.
In this work we investigate a class of string, compact Jacobi matrices with very rapidly decreasing weights. In particular, we have found Hellinger-Weyls function representation as ratio of two entire functions with known Taylor series representation. The asymptotical estimations of zeroes of this entire functions and of eigenvalues of a corresponding operator are found. The application of this theory to Rogers-Ramanujans functions is considered.Submitted: November 18, 2002 Revised: October 30, 2003 相似文献
932.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
933.
We proceed with our study of increasing self-described sequences F, beginning with 1 and defined by a functional equation
In [1] we exhibited the simple solution f (t)=Ct, for some (0,1), of the associated functional-differential equation
and we proved that provided <2/(2+d()), where
we have the asymtotic equivalence F(m)~ Cm.In the present paper we show that this last result is optimal, in the sense that the self-described sequence defined by |F–1(m)|=F(m)2, that is
for which the boundary case =2/(2+d())(=1/2) holds, does not satisfy F(m) ~ Cm. We also show that the m-th term F(m) of a sequence F for which the boundary case holds is nevertheless of asymptotic order m.Then we investigate the behaviour of self-described sequences F when lies beyond the boundary case. In [1] we established the estimates
when is the unique fixed point of a certain associated function. We were only able to prove in general that the latter holds when does not lie beyond the boundary case, however. In the present paper we prove that whenever
is the unique fixed point of this function, and in addition we obtain estimates more precise than (*). This applies for instance to the sequence defined by
that is
相似文献
934.
Hugh Thomas 《Algebra Universalis》2005,53(4):481-489
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [MT] by combining results of McNamara [Mc] and Liu [Li]. As part of our proof, we show that the maximum graded quotient of the free product of a chain and a single-element lattice is finite and distributive.Received May 24, 2004; accepted in final form October 12, 2004. 相似文献
935.
We relate the semiclassical asymptotics of the 6j symbols for the quantized enveloping algebra
at q a root of unity (resp. q real positive) to the geometry of spherical (resp. hyperbolic) tetrahedra. 相似文献
936.
In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be unbounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not exponentially stable systems to obtain the decay rate, which is not available in the literature.Received: July 21, 2003 相似文献
937.
Constrained diffusions, with diffusion matrix scaled by small ?>0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ?→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ?2 these moments are shown to asymptotically coalesce at an exponential rate. 相似文献
938.
In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way. 相似文献
939.
We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has ‘small’ local character in M or else M contains a measure of ‘large’ Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions. 相似文献
940.