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841.
Suppose thatX andY are real Banach spaces,U ⊂X is an open bounded set star-shaped with respect to some point,n, k ∈ ℕ,k <n, andMn, k (U,Y) is the sharp constant in the Markov type inequality for derivatives of polynomial mappings. It is proved that for anyM ≥M
n,k
(U, Y) there exists a constantB > 0 such that for any functionf ∈C
n
(U, Y) the following inequality holds:
The constantM =M
n−1,k
(U, Y) is best possible in the sense thatM
n−1,k
(U, Y) = infM, where inf is taken over allM such that for someB > 0 the estimate holds for allf ∈C
n
(U, Y).
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 332–342, March, 1998.
This research was partially supported by the International Science Foundation under grant No. U92000. and by the State Committee
of the Ukraine for Science and Technology. 相似文献
842.
B. P. Duggal 《Proceedings of the American Mathematical Society》1998,126(7):2047-2052
Given a Hilbert space , let be operators on . Anderson has proved that if is normal and , then for all operators . Using this inequality, Du Hong-Ke has recently shown that if (instead) , then for all operators . In this note we improve the Du Hong-Ke inequality to for all operators . Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms.
843.
We define trees generated by bi-infinite sequences, calculate their walk-invariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-infinite sequence with a simple random walk on an augmented Galton-Watson tree. We find that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree generated by a bi-infinite sequence. This is due to an inequality for random variables with values in [1, [ involving harmonic, geometric and arithmetic mean. 相似文献
844.
For each [0, 1] we consider the Dirichlet form
and the associated Dirichlet operator
for the Gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential. The Gibbs measure is related to the Gibbs state of the system via a (functional) Euclidean integral procedure. The configuration space for the spin systems is given by
We formulate Dirichlet forms in the framework of rigged Hilbert spaces which are related to the space . Under appropriate conditions on the potential, we show that the Dirichlet operator
is essentially self-adjoint on the domain of smooth cylinder functions. We give sufficient conditions on the potential so that the corresponding Gibbs measure is uniformly log-concave (ULC). This property gives the spectral gap of the Dirichlet operator
at the lower end of the spectrum. Furthermore, we prove that under the conditions of (ULC), the unique Gibbs measure satisfies the log-Sobolev inequality (LS). We use an approximate argument used in the study of the same subjects for loop spaces, which in turn is a modification of the method originally developed by S. Albeverio, Yu. G. Kondratiev, and M. Röckner. 相似文献
845.
846.
Takayuki Furuta Derming Wang 《Proceedings of the American Mathematical Society》1998,126(8):2427-2432
Let with and let and . As a generalization of a result due to Furuta, it is shown that the operator function
is decreasing for and if . Moreover, if and , then is decreasing for and . The latter result is an extension of an earlier result of Furuta.
847.
E. Grenier 《Proceedings of the American Mathematical Society》1998,126(2):523-530
We study the semi-classical limit of the nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.
848.
Gensun Fang 《中国科学A辑(英文版)》1998,41(12):1272-1277
The Nikolskii type inequality for cardinal splines
is proved, which is exact in the sense of order, where ∈ ℒ
m,h
, and ℒ
m,k
is the space of cardinal splines with nodes
Project supported by the National Natural Science Foundation of China (Grant No. 19671012), and Doctoral Programme Foundation
of Institution of Higher Education. 相似文献
849.
Hugo Aduén 《Journal of Mathematical Analysis and Applications》2008,337(1):348-359
Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k>0 large, there exist exactly two radial solutions with k nodal regions (connected components of ). The problem need not be homogeneous. 相似文献
850.
Gelu Popescu 《Journal of Functional Analysis》2008,254(4):1003-1057
In this paper, we initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space H, where m?2, n?2, and p is a positive regular polynomial in n noncommutative indeterminates. These domains are defined by certain positivity conditions on p, i.e.,