共查询到20条相似文献，搜索用时 93 毫秒
1.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
2.
The aim of this note is to prove the following theorem. Let
where P(ix) is a nonnegative homogeneous elliptic polynomial on R
d
and V is a nonnegative polynomial potential. Then for every 1 < p < ∞ and every α > 0 there exist constants C
1, C
2 > 0 such that
and
for f in the Schwartz class . We take advantage of the Christ inversion theorem for singular integral operators with a small amount of smoothness on
nilpotent Lie groups, the maximal subelliptic L
2-estimates for the generators of stable semi-groups of measures, and the principle of transference of Coifman–Weiss.
In memory of Tadek Pytlik, our teacher and friend.
Research supported by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic Analysis,
Nonlinear Analysis and Probability” MTKD-CT-2004-013389 and by Polish funds for science in years 2005–2008 (research project
1P03A03029). 相似文献
3.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
4.
Michael Winkler 《Mathematische Annalen》2007,339(3):559-597
This paper deals with nonnegative solutions of for
with and prescribed continuous Dirichlet data B = B(x) on ∂Ω. It is proved that for n ≤ 6 there is a critical parameter with the following property: If q > q
c
then there exist at least two continuous weak solutions emanating from some explicitly known stationary solution w: one that coincides with w and another one that satisfies u ≥ w but . For n ≤ 6 and q ≤ q
c
(or n ≥ 7), however, such a second solution above w is impossible. Moreover, it is shown that for n ≤ 6, q > q
c
and any sufficiently small nonnegative boundary data B there exist initial values admitting at least two continuous weak solutions of (Q). The final result asserts that for any
n and q nonuniqueness for (Q) holds at least for some boundary and initial data. 相似文献
5.
We present a norm estimate for the partial transpose map Θ on the tensor product
with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on Mm,n in terms of the spectral norm of
:
We show further that in the special case of
as well as AX + XB and AX + XBT those estimates are much improved and that
for certain Schatten p-norms.
Dedicated to the memory of late Professor Helmut H. Schaefer 相似文献
6.
Some Properties of Essential Spectra of a Positive Operator 总被引：1，自引：1，他引：0
Egor A. Alekhno 《Positivity》2007,11(3):375-386
Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T) of the operator T is a set
, where
is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum
are introduced in the article. The conditions by which
implies either
or
are investigated, where σef(T) is the Fredholm essential spectrum. By this reason, the relations between coefficients of the main part of the Laurent series
of the resolvent R(., T) of a positive operator T around of the point λ = r(T) are studied. The example of a positive integral operator T : L1→ L∞ which doesn’t dominate a non-zero compact operator, is adduced. Applications of results which are obtained, to the spectral
theory of band irreducible operators, are given. Namely, the criteria when the operator inequalities 0 ≤ S < T imply the spectral radius inequality r(S) < r(T), are established, where T is a band irreducible abstract integral operator. 相似文献
7.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
8.
E. S. Dubtsov 《Journal of Mathematical Sciences》2008,148(6):841-845
Let u be a strictly positive, harmonic Bloch function on the upper half-space ℝ
+
d+1
. Then the set
has the maximal Hausdorff dimension. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 105–112. 相似文献
9.
Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups
Wen-Bin Zhang 《The Ramanujan Journal》2008,15(1):47-75
We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic
semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let
be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in
with “degree” ∂(a)=m satisfies
with constants q>1, ρ
1<ρ
2<⋅⋅⋅<ρ
r
=ρ, ρ≥1, γ>1+ρ. For the main result, let α,τ,η be positive constants such that α>1,τ
ρ≥1, and τ
α
ρ≥1. Then for a multiplicative function f(a) on
the following two conditions (A) and (B) are equivalent. These are (A) All four series
converge and
and (B) The order τ
ρ mean-value
exists with m
f
≠0 and the limit
exists with M
v
(α)>0.
相似文献
10.
Aleksandar Ivić 《Archiv der Mathematik》2008,90(5):412-419
If
denotes the error term in the classical Rankin-Selberg problem, then it is proved that
where Δ1(x) = ∫
x
0 Δ(u)du. The latter bound is, up to ‘ɛ’, best possible.
Received: 8 February 2007 相似文献
11.
12.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
13.
E. G. Kwon 《Integral Equations and Operator Theory》2009,64(2):251-260
We characterize the composition operators mapping Blochs boundedly into the weighted Bergman spaces of logarithmic weight.
For 0 < p < ∞, 1 < α < ∞, let Ap, log α denote the space of holomorphic functions F in the unit disc D for which
and let Ap, log ασ denote the class of holomorphic self maps f of D for which
Then for the Bloch pullback operator Cf, the following are equivalent:
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion
Fund) (KRF-2007-313-C00026). 相似文献
| (1) | Cf maps Bloch space boundedly into A2p, log α |
| (2) | |
| (3) | . |
14.
We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space WN,2([0, ∞); e−x) and the Sobolev-Legendre space WN,2([−1, 1]) with respect to the Sobolev-Laguerre inner product
and with respect to the Sobolev-Legendre inner product
respectively, where a0 = 1, ak ≥0, 1 ≤k ≤N −1, γ > 0, and N ≥1 is an integer. 相似文献
15.
Pu Zhang 《数学学报(英文版)》2008,24(8):1387-1400
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,
｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.
The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.
The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
16.
A. I. Zvyagintsev 《Mathematical Notes》1997,62(5):596-606
For functions satisfying the boundary conditions
, the following inequality with sharp constants in additive form is proved:
wheren≥2, 0≤1≤n−2,−1≤m≤1, m+1≤n−3, and1≤p,q,r≤∞.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 712–724, November, 1997.
Translated by N. K. Kulman 相似文献
17.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
18.
We consider autonomous integrals
in the multidimensional calculus of variations, where the integrand f is a strictly W
1,p
-quasiconvex C
2-function satisfying the (p,q)-growth conditions
with exponents 1 < p ≤ q < ∞. Under these assumptions we establish an existence result for minimizers of F in provided . We prove a corresponding partial C
1,α
-regularity theorem for . This is the first regularity result for autonomous quasiconvex integrals with (p,q)-growth. 相似文献
19.
I. E. Chyzhykov 《Ukrainian Mathematical Journal》2007,59(7):1088-1109
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A
σ
ρ
of functions g(z) analytic in the unit disk
= {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 979–995, July, 2007. 相似文献
20.
We consider the following Liouville equation in
For each fixed and a
j
> 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior:
相似文献