共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
2.
An arithmetic function f is called a sieve function of range Q if its Eratosthenes transform g = f * μ is supported in [1,Q] ∩ N, where g(q) ? ε q ε (?ε > 0). We continue our study of the distribution of f(n) over short arithmetic bands, n ≡ ar + b (mod q), with n ∈ (N,2N] ∩ N, 1 ≤ a ≤ H = o(N) and r,b ∈ Z such that g:c:d:(r,q) = 1. In particular, the optimality of some results is discussed. 相似文献
3.
Ievgen V. Bondarenko Rostyslav V. Kravchenko 《Discrete and Computational Geometry》2011,46(2):389-393
Let A be an expanding integer n×n matrix and D be a finite subset of ? n . The self-affine set T=T(A,D) is the unique compact set satisfying the equality \(A(T)=\bigcup_{d\in D}(T+d)\). We present an effective algorithm to compute the Lebesgue measure of the self-affine set T, the measure of the intersection T∩(T+u) for u∈? n , and the measure of the intersection of self-affine sets T(A,D 1)∩T(A,D 2) for different sets D 1, D 2?? n . 相似文献
4.
For a normed algebra A and natural numbers k we introduce and investigate the ∥ · ∥ closed classes P k (A). We show that P1(A) is a subset of P k (A) for all k. If T in P1(A), then Tn lies in P1(A) for all natural n. If A is unital, U, V ∈ A are such that ∥U∥ = ∥V∥ = 1, VU = I and T lies in P k (A), then UTV lies in P k (A) for all natural k. Let A be unital, then 1) if an element T in P1(A) is right invertible, then any right inverse element T?1 lies in P1(A); 2) for ßßIßß = 1 the class P1(A) consists of normaloid elements; 3) if the spectrum of an element T, T ∈ P1(A) lies on the unit circle, then ∥TX∥ = ∥X∥ for all X ∈ A. If A = B(H), then the class P1(A) coincides with the set of all paranormal operators on a Hilbert space H. 相似文献
5.
We consider some class of non-linear systems of the form where A(·) ∈ ? n × n , A i (·) ∈ ? n × n , b(·) ∈ ? n , whose coefficients are arbitrary uniformly bounded functionals.
$\dot x = A( \cdot )x + \sum\limits_{i = 1}^l {A_i ( \cdot )x(t - \tau _i (t)) + b( \cdot )u} ,$
A special type of the Lyapunov-Krasovskii functional is used to synthesize dynamic control described by the equation where ρ(·) ∈ ?1, m(·) ∈ ? n , which makes the system globally asymptotically stable. Also, the situation is considered where the control u enters into the system not directly but through a pulse element performing an amplitude-frequency modulation.
相似文献
$\dot u = \rho ( \cdot )u + (m( \cdot ),x),$
6.
K. V. Storozhuk 《Siberian Mathematical Journal》2010,51(2):330-337
Let T t : X → X be a C 0-semigroup with generator A. We prove that if the abscissa of uniform boundedness of the resolvent s 0(A) is greater than zero then for each nondecreasing function h(s): ?+ → R + there are x′ ∈ X′ and x ∈ X satisfying ∫ 0 ∞ h(|〈x′, T x x〉|)dt = ∞. If i? ∩ Sp(A) ≠ Ø then such x may be taken in D(A ∞). 相似文献
7.
Let(T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote byω(x,f) and P(f) the ω-limit set of x under f and the set of periodic points of,respectively. Write Ω(x,f) = {y| there exist a sequence of points x_k E T and a sequence of positive integers n_1 n_2 … such that lim_(k→∞)x_k=x and lim_(k→∞)f~(n_k)(x_k) =y}. In this paper, we show that the following statements are equivalent:(1) f is equicontinuous.(2) ω(x, f) = Ω(x,f) for any x∈T.(3) ∩_(n=1)~∞f~n(T) = P(f),and ω(x,f)is a periodic orbit for every x ∈ T and map h : x→ω(x,f)(x ET)is continuous.(4) Ω(x,f) is a periodic orbit for any x∈T. 相似文献
8.
A. M. Bikchentaev 《Mathematical Notes》2016,100(3-4):515-525
Let τ be a faithful normal semifinite trace on a von Neumann algebra M, let p, 0 < p < ∞, be a number, and let Lp(M, τ) be the space of operators whose pth power is integrable (with respect to τ). Let P and Q be τ-measurable idempotents, and let A ≡ P ? Q. In this case, 1) if A ≥ 0, then A is a projection and QA = AQ = 0; 2) if P is quasinormal, then P is a projection; 3) if Q ∈ M and A ∈ Lp(M, τ), then A2 ∈ Lp(M, τ). Let n be a positive integer, n > 2, and A = An ∈ M. In this case, 1) if A ≠ 0, then the values of the nonincreasing rearrangement μt(A) belong to the set {0} ∪ [‖An?2‖?1, ‖A‖] for all t > 0; 2) either μt(A) ≥ 1 for all t > 0 or there is a t0 > 0 such that μt(A) = 0 for all t > t0. For every τ-measurable idempotent Q, there is aunique rank projection P ∈ M with QP = P, PQ = Q, and PM = QM. There is a unique decomposition Q = P + Z, where Z2 = 0, ZP = 0, and PZ = Z. Here, if Q ∈ Lp(M, τ), then P is integrable, and τ(Q) = τ(P) for p = 1. If A ∈ L1(M, τ) and if A = A3 and A ? A2 ∈ M, then τ(A) ∈ R. 相似文献
9.
V. N. Margaryan H. G. Ghazaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(5):211-220
A polynomial P(ξ) = P(ξ1,..., ξ n ) is said to be almost hypoelliptic if all its derivatives D ν P(ξ) can be estimated from above by P(ξ) (see [16]). By a theorem of Seidenberg-Tarski it follows that for each polynomial P(ξ) satisfying the condition P(ξ) > 0 for all ξ ∈ R n , there exist numbers σ > 0 and T ∈ R1 such that P(ξ) ≥ σ(1 + |ξ|) T for all ξ ∈ R n . The greatest of numbers T satisfying this condition, denoted by ST(P), is called Seidenberg-Tarski number of polynomial P. It is known that if, in addition, P ∈ I n , that is, |P(ξ)| → ∞ as |ξ| → ∞, then T = T(P) > 0. In this paper, for a class of almost hypoelliptic polynomials of n (≥ 2) variables we find a sufficient condition for ST(P) ≥ 1. Moreover, in the case n = 2, we prove that ST(P) ≥ 1 for any almost hypoelliptic polynomial P ∈ I2. 相似文献
10.
A. M. Bikchentaev 《Theoretical and Mathematical Physics》2018,195(1):557-562
Let ? be a trace on the unital C*-algebra A and M ? be the ideal of the definition of the trace ?. We obtain a C*analogue of the quantum Hall effect: if P,Q ∈ A are idempotents and P ? Q ∈ M ? , then ?((P ? Q)2n+1) = ?(P ? Q) ∈ R for all n ∈ N. Let the isometries U ∈ A and A = A*∈ A be such that I+A is invertible and U-A ∈ M ? with ?(U-A) ∈ R. Then I-A, I?U ∈ M ? and ?(I?U) ∈ R. Let n ∈ N, dimH = 2n + 1, the symmetry operators U, V ∈ B(H), and W = U ? V. Then the operator W is not a symmetry, and if V = V*, then the operator W is nonunitary. 相似文献
11.
Order-sharp estimates are established for the best N-term approximations of functions from Nikol’skii–Besov type classes Bpqsm(Tk) with respect to the multiple trigonometric system T(k) in the metric of Lr(Tk) for a number of relations between the parameters s, p, q, r, and m (s = (s1,..., sn) ∈ R+n, 1 ≤ p, q, r ≤ ∞, m = (m1,..., mn) ∈ Nn, k = m1 +... + mn). Constructive methods of nonlinear trigonometric approximation—variants of the so-called greedy algorithms—are used in the proofs of upper estimates. 相似文献
12.
V. I. Zenkov 《Siberian Mathematical Journal》2018,59(2):264-269
Given a finite group G with socle isomorphic to L n (2 m ), we describe (up to conjugacy) all ordered pairs of primary subgroups A and B in G such that A ∩ B g ≠ 1 for all g ∈ g. 相似文献
13.
Sara M. Motlaghian Ali Armandnejad Frank J. Hall 《Czechoslovak Mathematical Journal》2016,66(3):847-858
Let Mm,n be the set of all m × n real matrices. A matrix A ∈ Mm,n is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions T: Mm,n → Mm,n that preserve or strongly preserve row-dense matrices, i.e., T(A) is row-dense whenever A is row-dense or T(A) is row-dense if and only if A is row-dense, respectively. Similarly, a matrix A ∈ Mn,m is called a column-dense matrix if every column of A is a column-dense vector. At the end, the structure of linear preservers (strong linear preservers) of column-dense matrices is found. 相似文献
14.
An IP system is a functionn taking finite subsets ofN to a commutative, additive group Ω satisfyingn(α∪β)=n(α)+n(β) whenever α∩β=ø. In an extension of their Szemerédi theorem for finitely many commuting measure preserving transformations, Furstenberg and Katznelson showed that ifS i ,1≤i≤k, are IP systems into a commutative (possibly infinitely generated) group Ω of measure preserving transformations of a probability space (X, B, μ, andA∈B with μ(A)>0, then for some ø≠α one has μ(? i=1 k S i({α})A>0). We extend this to so-called FVIP systems, which are polynomial analogs of IP systems, thereby generalizing as well joint work by the author and V. Bergelson concerning special FVIP systems of the formS(α)=T(p(n(α))), wherep:Z t →Z d is a polynomial vanishing at zero,T is a measure preservingZ d action andn is an IP system intoZ t . The primary novelty here is potential infinite generation of the underlying group action, however there are new applications inZ d as well, for example multiple recurrence along a wide class ofgeneralized polynomials (very roughly, functions built out of regular polynomials by iterated use of the greatest integer function). 相似文献
15.
Let μ be a Radon measure on Rd which may be non–doubling. The only condition satisfied by μ is that μ(B(x, r)) ≤ Cr n for all x ∈ ? d , r > 0 and some fixed 0 < n ≤ d. In this paper, the authors prove that the boundedness from H 1(μ) into L 1,∞(μ) of a singular integral operator T with Calderón–Zygmund kernel of Hörmander type implies its L 2(μ)–boundedness. 相似文献
16.
David Seifert 《Journal d'Analyse Mathématique》2016,130(1):329-354
The Katznelson-Tzafriri Theorem states that, given a power-bounded operator T, ∥Tn(I ? T)∥ → 0 as n → ∞ if and only if the spectrum σ(T) of T intersects the unit circle T in at most the point 1. This paper investigates the rate at which decay takes place when σ(T) ∩ T = {1}. The results obtained lead, in particular, to both upper and lower bounds on this rate of decay in terms of the growth of the resolvent operator R(eiθ, T) as θ → 0. In the special case of polynomial resolvent growth, these bounds are then shown to be optimal for general Banach spaces but not in the Hilbert space case. 相似文献
17.
Yair Glasner 《Israel Journal of Mathematics》2017,219(1):215-270
Let Γ < GL n (F) be a countable non-amenable linear group with a simple, center free Zariski closure. Let Sub(Γ) denote the space of all subgroups of Γ with the compact, metric, Chabauty topology. An invariant random subgroup (IRS) of Γ is a conjugation invariant Borel probability measure on Sub(Γ). An IRS is called non-trivial if it does not have an atom in the trivial group, i.e. if it is non-trivial almost surely. We denote by IRS0(Γ) the collection of all non-trivial IRS on Γ.
Theorem 0.1: With the above notation, there exists a free subgroup F < Γ and a non-discrete group topology on Γ such that for every μ ∈ IRS0(Γ) the following properties hold:
Φ: (Sub(Γ), μ) → (Sub(F),Φ*μ) Δ → Δ ∩ F is an F-invariant isomorphism of probability spaces.A more technical version of this theorem is valid for general countable linear groups. We say that an action of Γ on a probability space, by measure preserving transformations, is almost surely non-free (ASNF) if almost all point stabilizers are non-trivial.Corollary 0.2: Let Γ be as in the Theorem above. Then the product of finitely many ASNF Γ-spaces, with the diagonal Γ action, is ASNF.Corollary 0.3: Let Γ < GLn(F) be a countable linear group, A Δ Γ the maximal normal amenable subgroup of Γ — its amenable radical. If μ ∈ IRS(Γ) is supported on amenable subgroups of Γ, then in fact it is supported on Sub(A). In particular, if A(Γ) = <e> then Δ = <e>, μ almost surely. 相似文献
μ-almost every subgroup of Γ is open
- F ·Δ = Γ for μ-almost every Δ ∈ Sub(Γ).
- F ∩ Δ is infinitely generated, for every open subgroup. In particular, this holds for μ-almost every Δ ∈ Sub(Γ).
- The map
18.
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and A(H) ? B(H) be a standard operator algebra which is closed under the adjoint operation. Let F: A(H)→ B(H) be a linear mapping satisfying F(AA*A) = F(A)A*A + Ad(A*)A + AA*d(A) for all A ∈ A(H), where the associated linear mapping d: A(H) → B(H) satisfies the relation d(AA*A) = d(A)A*A + Ad(A*)A + AA*d(A) for all A ∈ A(H). Then F is of the form F(A) = SA ? AT for all A ∈ A(H) and some S, T ∈ B(H), that is, F is a generalized derivation. We also prove some results concerning centralizers on A(H) and semisimple H*-algebras. 相似文献
19.
S. Wehmeier 《Lithuanian Mathematical Journal》2007,47(3):352-360
We show that the Erdös-Kac theorem for additive arithmetical semigroups can be proved under the condition that the counting function of elements has the asymptotics G(n) = q n (A + O(1/(lnn)k) as n → ∞ with A > 0, q > 1, and arbitrary k ∈ ? and that P(n) = O(q n /n) for the number of prime elements of degree n. This improves a result of Zhang. 相似文献