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1.
M. I. Gordin 《Journal of Mathematical Sciences》2000,99(2):1053-1060
Let T: X→X be an automorphism (a measurable invertible measure-preserving transformation) of a probability space (X, F, μ)
and let two μ-symmetric Markov generators Au and As acting on the space L2=L2 (X, F, μ) be “eigenfunctions” of the automorphism T with eigenvaluesθ
u
> 1 andθ
s
< 1, respectively. We construct an extension of the automorphism T having increasing and decreasing filtrations by means
of a transformation on the path space of these processes. Under additional conditions, we give an estimate of the maximal
correlation coefficient between the δ-fields chosen from these filtrations. Hyperbolic toral automorphisms are considered
as an example. Applications to limit theorems are given. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 61–72.
Translated by M. I. Gordin. 相似文献
2.
D. V. Yakubovich 《Journal of Mathematical Sciences》1997,87(5):3971-3979
Let T be a bounded linear operator in a separable Banach space X and let μ be a nonnegative measure in χ with compact support.
A function mT,μ is considered that is defined μ-a.e. and has nonnegative integers or +∞ as values. This function is called the local multiplicity
of T with respect to the measure μ. This function has some natural properties, it is invariant under similarity and quasisimilarity;
the local spectral multiplicity of a direct sum of operators equals the sum of local multiplicities, and so on. The definition
is given in terms of the maximal diagonalization of the operator T. It is shown that this diagonalization is unique in the
natural sense. A notion of a system of generalized eigenvectors, dual to the notion of diagonalization, is discussed. Some
examples of evaluation of the local spectral multiplicity function are given. Bibliography:10 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 293–306. 相似文献
3.
A. M. Vershik 《Journal of Mathematical Sciences》1997,87(6):4054-4058
For any ergodic transformation T of a Lebesgue space (X, μ), it is possible to introduce a topology τ on X such that (a) X becomes a totally disconnected compactum (a Cantor set) with a Markov structure, and μ becomes a Borel Markov measure;
(b) T becomes a minimal strictly ergodic homeomorphism of (X, τ); (c) the orbit partition of T is the tail partition of the Markov compactum (up to two classes of the partition). The Markov
compactum structure is the same as the path structure of the Bratteli diagram for some AF-algebra. Bibliography: 19 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 120–126. 相似文献
4.
E. M. Vechtomov 《Mathematical Notes》1997,62(5):575-580
The latticeA(X) of all possible subalgebras of the ring of all continuous ℝ-valued functions defined on an ℝ-separated spaceX is considered. A topological space is said to be a Hewitt space if it is homeomorphic to a closed subspace of a Tychonoff
power of the real line ℝ. The main achievement of the paper is the proof of the fact that any Hewitt spaceX is determined by the latticeA(X). An original technique of minimal and maximal subalgebras is applied. It is shown that the latticeA(X) is regular if and only ifX contains at most two points.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 687–693, November, 1997.
Translated by A. I. Shtern 相似文献
5.
N. M. Gulevich 《Journal of Mathematical Sciences》1996,81(2):2562-2566
For a Banach space X, a new constant G(X)=sup {λ(X) | A ⊂ X, d(A)=1} is introduced. The main result is that G (X) coincides with the Jung constant J (X) (Theorem 1), which
yields an estimate for the latter. Some other results concerning J (X) and the measure of nonconvexity λ are given. Bibliography:
5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 174–181.
Translated by O. A. Ivanov. 相似文献
6.
Yu. B. Farforovskaya 《Journal of Mathematical Sciences》1998,92(1):3640-3656
In this paper, conditions are considered for the existence of the double operator integral ∫∫ ϕ(λ,μ)dEλTdFμ, where Eλ, Fμ are the spectral functions of tow self-adjoint operators A, B on a Hilbert space and T is a bounded operator. In principal,
the case where A has finite spectrum is studied. Nonlinear estimates of ‖f(A)T-T f(B)‖ in terms of the norm of ‖AT-TB‖ for
f∈ Lip 1 are deduced. Also, a formula for the Fréchet derivative is presented. Bibliography: 16 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 148–173.
Translated by S. V. Kislyakov. 相似文献
7.
Let (K, μ) be a measurable space with μ(K)=1. Let Ip,q: Lp (K, μ)→Lq (K, μ) be the embedding operator. The Bernstein widths of Ip, q are considered. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 166–169.
Translated by S. V. Kislyakov. 相似文献
8.
A. J. Lazar 《Israel Journal of Mathematics》1969,7(4):357-364
LetX be a polyhedral Banach space whose dual is anL
1(μ) space for some measureμ. Then for each Banach spacesY ⊆Z and each compact operatorT: Y →X there exists a norm preserving compact extension
Z →X. 相似文献
9.
S. V. Kislyakov 《Journal of Mathematical Sciences》1981,16(3):1102-1108
Let A be a closed subalgebra of the complex Banach algebra C(S), containing the constant functions. We assume that one has
found a probability measureμ on S and a function F from L∞(μ) such that: 1)|F|= 1 a.e. relative to μ; 2) F
μ
ε A1; 3) F is a limit point of the unit ball of the algebra A in the topology δ(L∞(μ), L1(μ)). One proves in the paper that under these conditions the space A** contains a complement space, isometric to H∞. The measure μ and the function F, satisfying the conditions l)-3) indeed exist if the maximal ideal space of the algebra
A contains a non-one-point part (and it is very likely that such aμ. and F exist whenever the algebra A is not self-adjoint). Thus, the above-formulated result allows us to extend A. Pelczynski's
theorem (Ref, Zh. Mat., 1975, 1B894) regarding the space H∞ to a very broad class of uniform algebras.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 65, pp. 80–89, 1976. 相似文献
10.
Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) −1). We derive a fast algorithm to compute the coefficients. 相似文献
11.
Kh. Kh. Ruzimuradov 《Journal of Mathematical Sciences》1996,79(5):1320-1324
Let Λ be a unimodular lattice in ℝ2, μ a homogeneous minimum of Λ; let P(a,b)⊂ℝ2 be a rectangle with vertices at the points (a,0), ...(0,b), P(a, b)+X its image under the translation by a vector X ∈ ℝ2. We prove that there exists a sequence of positive numbers v1<v2<...<vk<... with
, such that for u>μ the rectangle P(u, vk)+X contains T=S(P)+R points of Λ, where |R|<5; here S(P) is the area of the rectangle. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 82–89.
Translated by O. A. Ivanov. 相似文献
12.
D. S. Anisimov 《Journal of Mathematical Sciences》2006,139(2):6363-6368
A version of Grothendieck’s inequality says that any bounded linear operator acting from a Banach lattice X to a Banach lattice
Y acts from X(ℓ2) to Y (ℓ2) as well. A similar statement is proved for Hardy-type subspaces in lattices of measurable functions. Namely, let X be a
Banach lattice of measurable functions on the circle, and let an operator T act from the corresponding subspace of analytic
functions XA to a Banach lattice Y or, if Y is also a lattice of measurable functions on the circle, to the quotient space Y/YA. Under certain mild conditions on the lattices involved, it is proved that T induces an operator acting from XA(ℓ2) to Y (ℓ2) or to Y/YA(ℓ2), respectively. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 5–16. 相似文献
13.
M. N. Yakovlev 《Journal of Mathematical Sciences》2000,101(4):3361-3364
The solvability conditions for the equation Tu+F(u)=0 are found in the case where the operator [T+F′(u)]−1 exists only for u∈K, where K is a cone in a Banach space X. An application concerning the solvability of boundary-value problems
for systems of second-order differential equations is provided.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 225–230.
Translated by L. Yu. Kolotilina. 相似文献
14.
A. A. Makhnev 《Mathematical Notes》2000,68(2):232-236
A set Δ of vertices of a generalized quadrangle of order (s, t) is said to be a hyperoval if any line intersects Δ in either 0, or 2 points. A hyperoval Δ is called an affine ovoid if
|Δ|=2st. It is well known that μ-subgraphs in triangular extensions of generalized quadrangles are hyperovals. In the present paper
we prove that ifS is a triangular extension forGQ(s, t) with totally regular point graph Γ such that μ=2st, thens is even, Γ is an τ-antipodal graph of diameter 3 with τ=1+s/2, and eithers=2, ort=s+2.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 266–271, August, 2000. 相似文献
15.
Any measure preserving endomorphism generates both a decreasing sequence of σ-algebras and an invertible extension. In this
paper we exhibit a dyadic measure preserving endomorphism (X,T,μ) such that the decreasing sequence of σ-algebras that it generates is not isomorphic to the standard decreasing sequence
of σ-algebras. However the invertible extension is isomorphic to the Bernoulli two shift. 相似文献
16.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1999,109(1):75-85
For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L
1 (μ), X) has denting points iffL
1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit
ball of ℓ(X, Y) are strongly extreme points. 相似文献
17.
V. V. Peller 《Journal of Mathematical Sciences》1981,16(3):1139-1149
The paper is devoted to the determination of an analog of J, von Neumann's inequality for the space Lp.The fundamental result of the paper is: If T is an absolute contraction in the space Lp(X,F,μ) (i.e., |T|L1≤1) and |T|L∞≤1) then for every polynomial ϕ one has
where S is the shift operator in the space. On the basis of this theorem, one finds a theorem on substitutions in the space
of multipliers. One gives applications of the inequality (1) to the weighted shift operators in the space It turns out that
under some natural restrictions on the weight, inequality (1) becomes an equality for such operators. One also presents a
proof of J. von Neumann's inequality based on the approximation of a contraction in a Hilbert space by unitary operators.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 65, pp. 133–148, 1976.
The author wishes to express his thanks to N. K. Nikol'skii for suggesting the problem and for his interest in the paper. 相似文献
18.
A. B. Venkov 《Journal of Mathematical Sciences》1995,77(3):3170-3177
In the standard Hilbert space L2(F; dμ) of even automorphic functions, where F is the fundamental domain of the modular group PSL(2, ℤ), a full system of
functions (in terms of classical analytic modular forms) is constructed, up to a finite-dimensional subspace. Therefore, in
particular, almost every Maass waveform can be represented by a series in analytic forms. Bibliography: 9 titles.
To O. A. Ladyzhenskaya on her jubilee
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 200, 1992, pp. 51–61.
Translated by A. B. Venkov. 相似文献
19.
B. Farkas 《Acta Mathematica Hungarica》2003,98(1-2):71-77
Given a measure space < Ω,m,μ >, a locally bounded, Hausdorff topological linear space < X, τ > and a real number 0<p<1, one can define the space Lp(Ω,m,μ,X), which is, under certain assumptions, a Fréchet space if endowed with a suitable topology. M.M. Day [1] has given a necessary
and sufficient condition, in terms of the properties of the measure space < Ω,m,μ >, for the dual of Lp(Ω,m,μ,C) to be trivial. In this paper a different proof along with a slight generalization is given for this result, using standard
and elementary measure theoretic arguments.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
Coenraad C.A. Labuschagne Valeria Marraffa 《Central European Journal of Mathematics》2010,8(1):148-157
Spaces of cone absolutely summing maps are generalizations of Bochner spaces L
p
(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space $
\mathcal{L}^1 \left[ {\sum ,cbf(X)} \right]
$
\mathcal{L}^1 \left[ {\sum ,cbf(X)} \right]
of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L
1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of $
\mathcal{L}^1 \left[ {\sum ,cbf(X)} \right]
$
\mathcal{L}^1 \left[ {\sum ,cbf(X)} \right]
, and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map.
We also describe these set-valued cone absolutely summing maps as those that map order-Pettis integrable functions to integrably
bounded set-valued functions. 相似文献